Solve 4s^2=(35-3-8s/5)^2

$$4 s ^ { 2 } = ( \frac { 35 - 3 - 8 s } { 5 } ) ^ { 2 }$$

Solve for s

$$s=-16$$

$$s = \frac{16}{9} = 1\frac{7}{9} \approx 1.777777778$$

Steps Using the Quadratic Formula

Subtract 3 from 35 to get 32.

$$4s^{2}=\left(\frac{32-8s}{5}\right)^{2}$$

To raise \frac{32-8s}{5} to a power, raise both numerator and denominator to the power and then divide.

$$4s^{2}=\frac{\left(32-8s\right)^{2}}{5^{2}}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(32-8s\right)^{2}.

$$4s^{2}=\frac{1024-512s+64s^{2}}{5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$4s^{2}=\frac{1024-512s+64s^{2}}{25}$$

Divide each term of 1024-512s+64s^{2} by 25 to get \frac{1024}{25}-\frac{512}{25}s+\frac{64}{25}s^{2}.

$$4s^{2}=\frac{1024}{25}-\frac{512}{25}s+\frac{64}{25}s^{2}$$

Subtract \frac{1024}{25} from both sides.

$$4s^{2}-\frac{1024}{25}=-\frac{512}{25}s+\frac{64}{25}s^{2}$$

Add \frac{512}{25}s to both sides.

$$4s^{2}-\frac{1024}{25}+\frac{512}{25}s=\frac{64}{25}s^{2}$$

Subtract \frac{64}{25}s^{2} from both sides.

$$4s^{2}-\frac{1024}{25}+\frac{512}{25}s-\frac{64}{25}s^{2}=0$$

Combine 4s^{2} and -\frac{64}{25}s^{2} to get \frac{36}{25}s^{2}.

$$\frac{36}{25}s^{2}-\frac{1024}{25}+\frac{512}{25}s=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$\frac{36}{25}s^{2}+\frac{512}{25}s-\frac{1024}{25}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{36}{25} for a, \frac{512}{25} for b, and -\frac{1024}{25} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$s=\frac{-\frac{512}{25}±\sqrt{\left(\frac{512}{25}\right)^{2}-4\times \frac{36}{25}\left(-\frac{1024}{25}\right)}}{2\times \frac{36}{25}}$$

Square \frac{512}{25} by squaring both the numerator and the denominator of the fraction.

$$s=\frac{-\frac{512}{25}±\sqrt{\frac{262144}{625}-4\times \frac{36}{25}\left(-\frac{1024}{25}\right)}}{2\times \frac{36}{25}}$$

Multiply -4 times \frac{36}{25}.

$$s=\frac{-\frac{512}{25}±\sqrt{\frac{262144}{625}-\frac{144}{25}\left(-\frac{1024}{25}\right)}}{2\times \frac{36}{25}}$$

Multiply -\frac{144}{25} times -\frac{1024}{25} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$s=\frac{-\frac{512}{25}±\sqrt{\frac{262144+147456}{625}}}{2\times \frac{36}{25}}$$

Add \frac{262144}{625} to \frac{147456}{625} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$s=\frac{-\frac{512}{25}±\sqrt{\frac{16384}{25}}}{2\times \frac{36}{25}}$$

Take the square root of \frac{16384}{25}.

$$s=\frac{-\frac{512}{25}±\frac{128}{5}}{2\times \frac{36}{25}}$$

Multiply 2 times \frac{36}{25}.

$$s=\frac{-\frac{512}{25}±\frac{128}{5}}{\frac{72}{25}}$$

Now solve the equation s=\frac{-\frac{512}{25}±\frac{128}{5}}{\frac{72}{25}} when ± is plus. Add -\frac{512}{25} to \frac{128}{5} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$s=\frac{\frac{128}{25}}{\frac{72}{25}}$$

Divide \frac{128}{25} by \frac{72}{25} by multiplying \frac{128}{25} by the reciprocal of \frac{72}{25}.

$$s=\frac{16}{9}$$

Now solve the equation s=\frac{-\frac{512}{25}±\frac{128}{5}}{\frac{72}{25}} when ± is minus. Subtract \frac{128}{5} from -\frac{512}{25} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$s=-\frac{\frac{1152}{25}}{\frac{72}{25}}$$

Divide -\frac{1152}{25} by \frac{72}{25} by multiplying -\frac{1152}{25} by the reciprocal of \frac{72}{25}.

$$s=-16$$

The equation is now solved.

$$s=\frac{16}{9} s=-16$$

Steps for Completing the Square

Subtract 3 from 35 to get 32.

$$4s^{2}=\left(\frac{32-8s}{5}\right)^{2}$$

To raise \frac{32-8s}{5} to a power, raise both numerator and denominator to the power and then divide.

$$4s^{2}=\frac{\left(32-8s\right)^{2}}{5^{2}}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(32-8s\right)^{2}.

$$4s^{2}=\frac{1024-512s+64s^{2}}{5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$4s^{2}=\frac{1024-512s+64s^{2}}{25}$$

Divide each term of 1024-512s+64s^{2} by 25 to get \frac{1024}{25}-\frac{512}{25}s+\frac{64}{25}s^{2}.

$$4s^{2}=\frac{1024}{25}-\frac{512}{25}s+\frac{64}{25}s^{2}$$

Add \frac{512}{25}s to both sides.

$$4s^{2}+\frac{512}{25}s=\frac{1024}{25}+\frac{64}{25}s^{2}$$

Subtract \frac{64}{25}s^{2} from both sides.

$$4s^{2}+\frac{512}{25}s-\frac{64}{25}s^{2}=\frac{1024}{25}$$

Combine 4s^{2} and -\frac{64}{25}s^{2} to get \frac{36}{25}s^{2}.

$$\frac{36}{25}s^{2}+\frac{512}{25}s=\frac{1024}{25}$$

Divide both sides of the equation by \frac{36}{25}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{36}{25}s^{2}+\frac{512}{25}s}{\frac{36}{25}}=\frac{\frac{1024}{25}}{\frac{36}{25}}$$

Dividing by \frac{36}{25} undoes the multiplication by \frac{36}{25}.

$$s^{2}+\frac{\frac{512}{25}}{\frac{36}{25}}s=\frac{\frac{1024}{25}}{\frac{36}{25}}$$

Divide \frac{512}{25} by \frac{36}{25} by multiplying \frac{512}{25} by the reciprocal of \frac{36}{25}.

$$s^{2}+\frac{128}{9}s=\frac{\frac{1024}{25}}{\frac{36}{25}}$$

Divide \frac{1024}{25} by \frac{36}{25} by multiplying \frac{1024}{25} by the reciprocal of \frac{36}{25}.

$$s^{2}+\frac{128}{9}s=\frac{256}{9}$$

Divide \frac{128}{9}, the coefficient of the x term, by 2 to get \frac{64}{9}. Then add the square of \frac{64}{9} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$s^{2}+\frac{128}{9}s+\left(\frac{64}{9}\right)^{2}=\frac{256}{9}+\left(\frac{64}{9}\right)^{2}$$

Square \frac{64}{9} by squaring both the numerator and the denominator of the fraction.

$$s^{2}+\frac{128}{9}s+\frac{4096}{81}=\frac{256}{9}+\frac{4096}{81}$$

Add \frac{256}{9} to \frac{4096}{81} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$s^{2}+\frac{128}{9}s+\frac{4096}{81}=\frac{6400}{81}$$

Factor s^{2}+\frac{128}{9}s+\frac{4096}{81}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(s+\frac{64}{9}\right)^{2}=\frac{6400}{81}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(s+\frac{64}{9}\right)^{2}}=\sqrt{\frac{6400}{81}}$$

Simplify.

$$s+\frac{64}{9}=\frac{80}{9} s+\frac{64}{9}=-\frac{80}{9}$$

Subtract \frac{64}{9} from both sides of the equation.

$$s=\frac{16}{9} s=-16$$