Solve 0=-5*65*10^8x^2+5*65*10^8x+10

$$0 = - 5 \cdot 65 \times 10 ^ { 8 } x ^ { 2 } + 5 \cdot 65 \times 10 ^ { 8 } x + 10$$

Solve for x

$$x=\frac{\sqrt{105625000130}}{650000}+\frac{1}{2}\approx 1$$

$$x=-\frac{\sqrt{105625000130}}{650000}+\frac{1}{2}\approx -3.076923161 \cdot 10^{-10}$$

Steps Using the Quadratic Formula

Do the multiplications.

$$0=-325\times 10^{8}x^{2}+325\times 10^{8}x+10$$

Calculate 10 to the power of 8 and get 100000000.

$$0=-325\times 100000000x^{2}+325\times 10^{8}x+10$$

Multiply -325 and 100000000 to get -32500000000.

$$0=-32500000000x^{2}+325\times 10^{8}x+10$$

Calculate 10 to the power of 8 and get 100000000.

$$0=-32500000000x^{2}+325\times 100000000x+10$$

Multiply 325 and 100000000 to get 32500000000.

$$0=-32500000000x^{2}[phone]x+10$$

Swap sides so that all variable terms are on the left hand side.

$$-32500000000x^{2}[phone]x+10=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -32500000000 for a, 32500000000 for b, and 10 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-32500000000±\sqrt{32500000000^{2}-4\left(-32500000000\right)\times 10}}{2\left(-32500000000\right)}$$

Square 32500000000.

$$x=\frac{-32500000000±\sqrt{1056250000000000000000-4\left(-32500000000\right)\times 10}}{2\left(-32500000000\right)}$$

Multiply -4 times -32500000000.

$$x=\frac{-32500000000±\sqrt{1056250000000000000000+130000000000\times 10}}{2\left(-32500000000\right)}$$

Multiply 130000000000 times 10.

$$x=\frac{-32500000000±\sqrt{1056250000000000000000+1300000000000}}{2\left(-32500000000\right)}$$

Add 1056250000000000000000 to 1300000000000.

$$x=\frac{-32500000000±\sqrt{1056250001300000000000}}{2\left(-32500000000\right)}$$

Take the square root of 1056250001300000000000.

$$x=\frac{-32500000000±100000\sqrt{105625000130}}{2\left(-32500000000\right)}$$

Multiply 2 times -32500000000.

$$x=\frac{-32500000000±100000\sqrt{105625000130}}{-65000000000}$$

Now solve the equation x=\frac{-32500000000±100000\sqrt{105625000130}}{-65000000000} when ± is plus. Add -32500000000 to 100000\sqrt{105625000130}.

$$x=\frac{100000\sqrt{105625000130}-32500000000}{-65000000000}$$

Divide -32500000000+100000\sqrt{105625000130} by -65000000000.

$$x=-\frac{\sqrt{105625000130}}{650000}+\frac{1}{2}$$

Now solve the equation x=\frac{-32500000000±100000\sqrt{105625000130}}{-65000000000} when ± is minus. Subtract 100000\sqrt{105625000130} from -32500000000.

$$x=\frac{-100000\sqrt{105625000130}-32500000000}{-65000000000}$$

Divide -32500000000-100000\sqrt{105625000130} by -65000000000.

$$x=\frac{\sqrt{105625000130}}{650000}+\frac{1}{2}$$

The equation is now solved.

$$x=-\frac{\sqrt{105625000130}}{650000}+\frac{1}{2} x=\frac{\sqrt{105625000130}}{650000}+\frac{1}{2}$$

Steps for Completing the Square

Do the multiplications.

$$0=-325\times 10^{8}x^{2}+325\times 10^{8}x+10$$

Calculate 10 to the power of 8 and get 100000000.

$$0=-325\times 100000000x^{2}+325\times 10^{8}x+10$$

Multiply -325 and 100000000 to get -32500000000.

$$0=-32500000000x^{2}+325\times 10^{8}x+10$$

Calculate 10 to the power of 8 and get 100000000.

$$0=-32500000000x^{2}+325\times 100000000x+10$$

Multiply 325 and 100000000 to get 32500000000.

$$0=-32500000000x^{2}[phone]x+10$$

Swap sides so that all variable terms are on the left hand side.

$$-32500000000x^{2}[phone]x+10=0$$

Subtract 10 from both sides. Anything subtracted from zero gives its negation.

$$-32500000000x^{2}[phone]x=-10$$

Divide both sides by -32500000000.

$$\frac{-32500000000x^{2}[phone]x}{-32500000000}=-\frac{10}{-32500000000}$$

Dividing by -32500000000 undoes the multiplication by -32500000000.

$$x^{2}+\frac{32500000000}{-32500000000}x=-\frac{10}{-32500000000}$$

Divide 32500000000 by -32500000000.

$$x^{2}-x=-\frac{10}{-32500000000}$$

Reduce the fraction \frac{-10}{-32500000000} to lowest terms by extracting and canceling out 10.

$$x^{2}-x=\frac{1}{3250000000}$$

Divide -1, the coefficient of the x term, by 2 to get -\frac{1}{2}. Then add the square of -\frac{1}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-x+\left(-\frac{1}{2}\right)^{2}=\frac{1}{3250000000}+\left(-\frac{1}{2}\right)^{2}$$

Square -\frac{1}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-x+\frac{1}{4}=\frac{1}{3250000000}+\frac{1}{4}$$

Add \frac{1}{3250000000} to \frac{1}{4} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}-x+\frac{1}{4}=\frac{812500001}{3250000000}$$

Factor x^{2}-x+\frac{1}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{1}{2}\right)^{2}=\frac{812500001}{3250000000}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{1}{2}\right)^{2}}=\sqrt{\frac{812500001}{3250000000}}$$

Simplify.

$$x-\frac{1}{2}=\frac{\sqrt{105625000130}}{650000} x-\frac{1}{2}=-\frac{\sqrt{105625000130}}{650000}$$

Add \frac{1}{2} to both sides of the equation.

$$x=\frac{\sqrt{105625000130}}{650000}+\frac{1}{2} x=-\frac{\sqrt{105625000130}}{650000}+\frac{1}{2}$$