Solve 1600-x^2=1456

$$1600 - x ^ { 2 } = 1456$$

Solve for x

$$x=12$$

$$x=-12$$

Steps by Finding Square Root

Subtract 1600 from both sides.

$$-x^{2}=1456-1600$$

Subtract 1600 from 1456 to get -144.

$$-x^{2}=-144$$

Divide both sides by -1.

$$x^{2}=\frac{-144}{-1}$$

Fraction \frac{-144}{-1} can be simplified to 144 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=144$$

Take the square root of both sides of the equation.

$$x=12 x=-12$$

Steps Using the Quadratic Formula

Subtract 1456 from both sides.

$$1600-x^{2}-1456=0$$

Subtract 1456 from 1600 to get 144.

$$144-x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-x^{2}+144=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 144 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 144}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 144}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 144}}{2\left(-1\right)}$$

Multiply 4 times 144.

$$x=\frac{0±\sqrt{576}}{2\left(-1\right)}$$

Take the square root of 576.

$$x=\frac{0±24}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±24}{-2}$$

Now solve the equation x=\frac{0±24}{-2} when ± is plus. Divide 24 by -2.

$$x=-12$$

Now solve the equation x=\frac{0±24}{-2} when ± is minus. Divide -24 by -2.

$$x=12$$

The equation is now solved.

$$x=-12 x=12$$