Solve 169-y^2=0

$$169 - y ^ { 2 } = 0$$

Solve for y

$$y=13$$

$$y=-13$$

Steps by Finding Square Root

Subtract 169 from both sides. Anything subtracted from zero gives its negation.

$$-y^{2}=-169$$

Divide both sides by -1.

$$y^{2}=\frac{-169}{-1}$$

Fraction \frac{-169}{-1} can be simplified to 169 by removing the negative sign from both the numerator and the denominator.

$$y^{2}=169$$

Take the square root of both sides of the equation.

$$y=13 y=-13$$

Steps Using the Quadratic Formula

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.

$$-y^{2}+169=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 169 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 169}}{2\left(-1\right)}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-1\right)\times 169}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$y=\frac{0±\sqrt{4\times 169}}{2\left(-1\right)}$$

Multiply 4 times 169.

$$y=\frac{0±\sqrt{676}}{2\left(-1\right)}$$

Take the square root of 676.

$$y=\frac{0±26}{2\left(-1\right)}$$

Multiply 2 times -1.

$$y=\frac{0±26}{-2}$$

Now solve the equation y=\frac{0±26}{-2} when ± is plus. Divide 26 by -2.

$$y=-13$$

Now solve the equation y=\frac{0±26}{-2} when ± is minus. Divide -26 by -2.

$$y=13$$

The equation is now solved.

$$y=-13 y=13$$