Solve 913=81+x^2-8x

$$913 = 81 + x ^ { 2 } - 8 x$$

Solve for x

$$x=4\sqrt{53}+4\approx 33.120439557$$

$$x=4-4\sqrt{53}\approx -25.120439557$$

Steps Using the Quadratic Formula

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

$$81+x^{2}-8x=913$$

Subtract 913 from both sides.

$$81+x^{2}-8x-913=0$$

Subtract 913 from 81 to get -832.

$$-832+x^{2}-8x=0$$

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.

$$x^{2}-8x-832=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -8 for b, and -832 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\left(-832\right)}}{2}$$

Square -8.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\left(-832\right)}}{2}$$

Multiply -4 times -832.

$$x=\frac{-\left(-8\right)±\sqrt{64+3328}}{2}$$

Add 64 to 3328.

$$x=\frac{-\left(-8\right)±\sqrt{3392}}{2}$$

Take the square root of 3392.

$$x=\frac{-\left(-8\right)±8\sqrt{53}}{2}$$

The opposite of -8 is 8.

$$x=\frac{8±8\sqrt{53}}{2}$$

Now solve the equation x=\frac{8±8\sqrt{53}}{2} when ± is plus. Add 8 to 8\sqrt{53}.

$$x=\frac{8\sqrt{53}+8}{2}$$

Divide 8+8\sqrt{53} by 2.

$$x=4\sqrt{53}+4$$

Now solve the equation x=\frac{8±8\sqrt{53}}{2} when ± is minus. Subtract 8\sqrt{53} from 8.

$$x=\frac{8-8\sqrt{53}}{2}$$

Divide 8-8\sqrt{53} by 2.

$$x=4-4\sqrt{53}$$

The equation is now solved.

$$x=4\sqrt{53}+4 x=4-4\sqrt{53}$$

Steps for Completing the Square

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

$$81+x^{2}-8x=913$$

Subtract 81 from both sides.

$$x^{2}-8x=913-81$$

Subtract 81 from 913 to get 832.

$$x^{2}-8x=832$$

Divide -8, the coefficient of the x term, by 2 to get -4. Then add the square of -4 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-8x+\left(-4\right)^{2}=832+\left(-4\right)^{2}$$

Square -4.

$$x^{2}-8x+16=832+16$$

Add 832 to 16.

$$x^{2}-8x+16=848$$

Factor x^{2}-8x+16. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-4\right)^{2}=848$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-4\right)^{2}}=\sqrt{848}$$

Simplify.

$$x-4=4\sqrt{53} x-4=-4\sqrt{53}$$

Add 4 to both sides of the equation.

$$x=4\sqrt{53}+4 x=4-4\sqrt{53}$$