Solve x^2-2x*10^5+12*10^8=0

$$x ^ { 2 } - 2 x \times 10 ^ { 5 } + 12 \times 10 ^ { 8 } = 0$$

Solve for x

$$x=20000\sqrt{22}+100000\approx 193808.315196469$$

$$x=100000-20000\sqrt{22}\approx 6191.684803531$$

Steps Using the Quadratic Formula

Calculate 10 to the power of 5 and get 100000.

$$x^{2}-2x\times 100000+12\times 10^{8}=0$$

Multiply 2 and 100000 to get 200000.

$$x^{2}-200000x+12\times 10^{8}=0$$

Calculate 10 to the power of 8 and get 100000000.

$$x^{2}-200000x+12\times 100000000=0$$

Multiply 12 and 100000000 to get 1200000000.

$$x^{2}-200000x+1200000000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -200000 for b, and 1200000000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-200000\right)±\sqrt{\left(-200000\right)^{2}-4\times 1200000000}}{2}$$

Square -200000.

$$x=\frac{-\left(-200000\right)±\sqrt{40000000000-4\times 1200000000}}{2}$$

Multiply -4 times 1200000000.

$$x=\frac{-\left(-200000\right)±\sqrt{40000000000-4800000000}}{2}$$

Add 40000000000 to -4800000000.

$$x=\frac{-\left(-200000\right)±\sqrt{35200000000}}{2}$$

Take the square root of 35200000000.

$$x=\frac{-\left(-200000\right)±40000\sqrt{22}}{2}$$

The opposite of -200000 is 200000.

$$x=\frac{200000±40000\sqrt{22}}{2}$$

Now solve the equation x=\frac{200000±40000\sqrt{22}}{2} when ± is plus. Add 200000 to 40000\sqrt{22}.

$$x=\frac{40000\sqrt{22}+200000}{2}$$

Divide 200000+40000\sqrt{22} by 2.

$$x=20000\sqrt{22}+100000$$

Now solve the equation x=\frac{200000±40000\sqrt{22}}{2} when ± is minus. Subtract 40000\sqrt{22} from 200000.

$$x=\frac{200000-40000\sqrt{22}}{2}$$

Divide 200000-40000\sqrt{22} by 2.

$$x=100000-20000\sqrt{22}$$

The equation is now solved.

$$x=20000\sqrt{22}+100000 x=100000-20000\sqrt{22}$$

Steps for Completing the Square

Calculate 10 to the power of 5 and get 100000.

$$x^{2}-2x\times 100000+12\times 10^{8}=0$$

Multiply 2 and 100000 to get 200000.

$$x^{2}-200000x+12\times 10^{8}=0$$

Calculate 10 to the power of 8 and get 100000000.

$$x^{2}-200000x+12\times 100000000=0$$

Multiply 12 and 100000000 to get 1200000000.

$$x^{2}-200000x+1200000000=0$$

Subtract 1200000000 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}-200000x=-1200000000$$

Divide -200000, the coefficient of the x term, by 2 to get -100000. Then add the square of -100000 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-200000x+\left(-100000\right)^{2}=-1200000000+\left(-100000\right)^{2}$$

Square -100000.

$$x^{2}-200000x+10000000000=-1200000000+10000000000$$

Add -1200000000 to 10000000000.

$$x^{2}-200000x+10000000000=8800000000$$

Factor x^{2}-200000x+10000000000. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-100000\right)^{2}=8800000000$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-100000\right)^{2}}=\sqrt{8800000000}$$

Simplify.

$$x-100000=20000\sqrt{22} x-100000=-20000\sqrt{22}$$

Add 100000 to both sides of the equation.

$$x=20000\sqrt{22}+100000 x=100000-20000\sqrt{22}$$