Solve d^2-50=0

$$d ^ { 2 } - 50 = 0$$

Solve for d

$$d=5\sqrt{2}\approx 7.071067812$$

$$d=-5\sqrt{2}\approx -7.071067812$$

Steps by Finding Square Root

Add 50 to both sides. Anything plus zero gives itself.

$$d^{2}=50$$

Take the square root of both sides of the equation.

$$d=5\sqrt{2} d=-5\sqrt{2}$$

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.

$$d^{2}-50=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -50 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$d=\frac{0±\sqrt{0^{2}-4\left(-50\right)}}{2}$$

Square 0.

$$d=\frac{0±\sqrt{-4\left(-50\right)}}{2}$$

Multiply -4 times -50.

$$d=\frac{0±\sqrt{200}}{2}$$

Take the square root of 200.

$$d=\frac{0±10\sqrt{2}}{2}$$

Now solve the equation d=\frac{0±10\sqrt{2}}{2} when ± is plus.

$$d=5\sqrt{2}$$

Now solve the equation d=\frac{0±10\sqrt{2}}{2} when ± is minus.

$$d=-5\sqrt{2}$$

The equation is now solved.

$$d=5\sqrt{2} d=-5\sqrt{2}$$