Solve (0.01)x^2+left(7.225*10^-3right)x-7*225*10^-3=0

$$(0.01) { x }^{ 2 } + \left( 7.225 \times { 10 }^{ -3 } \right) x-7 \cdot 225 \times { 10 }^{ -3 } = 0$$

Solve for x

$$x = \frac{\sqrt{100883521} - 289}{800} \approx 12.193848628$$

$$x=\frac{-\sqrt{100883521}-289}{800}\approx -12.916348628$$

Steps Using the Quadratic Formula

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$0.01x^{2}+7.225\times \frac{1}{1000}x-7\times 225\times 10^{-3}=0$$

Multiply 7.225 and \frac{1}{1000} to get \frac{289}{40000}.

$$0.01x^{2}+\frac{289}{40000}x-7\times 225\times 10^{-3}=0$$

Multiply 7 and 225 to get 1575.

$$0.01x^{2}+\frac{289}{40000}x-1575\times 10^{-3}=0$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$0.01x^{2}+\frac{289}{40000}x-1575\times \frac{1}{1000}=0$$

Multiply 1575 and \frac{1}{1000} to get \frac{63}{40}.

$$0.01x^{2}+\frac{289}{40000}x-\frac{63}{40}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 0.01 for a, \frac{289}{40000} for b, and -\frac{63}{40} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\frac{289}{40000}±\sqrt{\left(\frac{289}{40000}\right)^{2}-4\times 0.01\left(-\frac{63}{40}\right)}}{2\times 0.01}$$

Square \frac{289}{40000} by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-\frac{289}{40000}±\sqrt{\frac{83521}{1600000000}-4\times 0.01\left(-\frac{63}{40}\right)}}{2\times 0.01}$$

Multiply -4 times 0.01.

$$x=\frac{-\frac{289}{40000}±\sqrt{\frac{83521}{1600000000}-0.04\left(-\frac{63}{40}\right)}}{2\times 0.01}$$

Multiply -0.04 times -\frac{63}{40} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-\frac{289}{40000}±\sqrt{\frac{83521}{1600000000}+\frac{63}{1000}}}{2\times 0.01}$$

Add \frac{83521}{1600000000} to \frac{63}{1000} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-\frac{289}{40000}±\sqrt{\frac{100883521}{1600000000}}}{2\times 0.01}$$

Take the square root of \frac{100883521}{1600000000}.

$$x=\frac{-\frac{289}{40000}±\frac{\sqrt{100883521}}{40000}}{2\times 0.01}$$

Multiply 2 times 0.01.

$$x=\frac{-\frac{289}{40000}±\frac{\sqrt{100883521}}{40000}}{0.02}$$

Now solve the equation x=\frac{-\frac{289}{40000}±\frac{\sqrt{100883521}}{40000}}{0.02} when ± is plus. Add -\frac{289}{40000} to \frac{\sqrt{100883521}}{40000}.

$$x=\frac{\sqrt{100883521}-289}{0.02\times 40000}$$

Divide \frac{-289+\sqrt{100883521}}{40000} by 0.02 by multiplying \frac{-289+\sqrt{100883521}}{40000} by the reciprocal of 0.02.

$$x=\frac{\sqrt{100883521}-289}{800}$$

Now solve the equation x=\frac{-\frac{289}{40000}±\frac{\sqrt{100883521}}{40000}}{0.02} when ± is minus. Subtract \frac{\sqrt{100883521}}{40000} from -\frac{289}{40000}.

$$x=\frac{-\sqrt{100883521}-289}{0.02\times 40000}$$

Divide \frac{-289-\sqrt{100883521}}{40000} by 0.02 by multiplying \frac{-289-\sqrt{100883521}}{40000} by the reciprocal of 0.02.

$$x=\frac{-\sqrt{100883521}-289}{800}$$

The equation is now solved.

$$x=\frac{\sqrt{100883521}-289}{800} x=\frac{-\sqrt{100883521}-289}{800}$$

Steps for Completing the Square

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$0.01x^{2}+7.225\times \frac{1}{1000}x-7\times 225\times 10^{-3}=0$$

Multiply 7.225 and \frac{1}{1000} to get \frac{289}{40000}.

$$0.01x^{2}+\frac{289}{40000}x-7\times 225\times 10^{-3}=0$$

Multiply 7 and 225 to get 1575.

$$0.01x^{2}+\frac{289}{40000}x-1575\times 10^{-3}=0$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$0.01x^{2}+\frac{289}{40000}x-1575\times \frac{1}{1000}=0$$

Multiply 1575 and \frac{1}{1000} to get \frac{63}{40}.

$$0.01x^{2}+\frac{289}{40000}x-\frac{63}{40}=0$$

Add \frac{63}{40} to both sides. Anything plus zero gives itself.

$$0.01x^{2}+\frac{289}{40000}x=\frac{63}{40}$$

Multiply both sides by 100.

$$\frac{0.01x^{2}+\frac{289}{40000}x}{0.01}=\frac{\frac{63}{40}}{0.01}$$

Dividing by 0.01 undoes the multiplication by 0.01.

$$x^{2}+\frac{\frac{289}{40000}}{0.01}x=\frac{\frac{63}{40}}{0.01}$$

Divide \frac{289}{40000} by 0.01 by multiplying \frac{289}{40000} by the reciprocal of 0.01.

$$x^{2}+\frac{289}{400}x=\frac{\frac{63}{40}}{0.01}$$

Divide \frac{63}{40} by 0.01 by multiplying \frac{63}{40} by the reciprocal of 0.01.

$$x^{2}+\frac{289}{400}x=\frac{315}{2}$$

Divide \frac{289}{400}, the coefficient of the x term, by 2 to get \frac{289}{800}. Then add the square of \frac{289}{800} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{289}{400}x+\left(\frac{289}{800}\right)^{2}=\frac{315}{2}+\left(\frac{289}{800}\right)^{2}$$

Square \frac{289}{800} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{289}{400}x+\frac{83521}{640000}=\frac{315}{2}+\frac{83521}{640000}$$

Add \frac{315}{2} to \frac{83521}{640000} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+\frac{289}{400}x+\frac{83521}{640000}=\frac{100883521}{640000}$$

Factor x^{2}+\frac{289}{400}x+\frac{83521}{640000}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{289}{800}\right)^{2}=\frac{100883521}{640000}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{289}{800}\right)^{2}}=\sqrt{\frac{100883521}{640000}}$$

Simplify.

$$x+\frac{289}{800}=\frac{\sqrt{100883521}}{800} x+\frac{289}{800}=-\frac{\sqrt{100883521}}{800}$$

Subtract \frac{289}{800} from both sides of the equation.

$$x=\frac{\sqrt{100883521}-289}{800} x=\frac{-\sqrt{100883521}-289}{800}$$