Solve Matrix

$$\left. \begin{array} { l } { \text { Solve the equation } 2 x ^ { 2 } + 50 = 0 \text { . } } \\ { \left. \begin{array} { l l } { \text { a. } x = \pm 5 } & { \text { c. } x = 5 \pm i } \end{array} \right. } \end{array} \right.$$

Solve for x

$$x=-5i$$

$$x=5i$$

Steps by Finding Square Root

Subtract 50 from both sides. Anything subtracted from zero gives its negation.

$$2x^{2}=-50$$

Divide both sides by 2.

$$x^{2}=\frac{-50}{2}$$

Divide -50 by 2 to get -25.

$$x^{2}=-25$$

The equation is now solved.

$$x=5i x=-5i$$

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.

$$2x^{2}+50=0$$

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

$$x=\frac{0±\sqrt{0^{2}-4\times 2\times 50}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\times 50}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\times 50}}{2\times 2}$$

Multiply -8 times 50.

$$x=\frac{0±\sqrt{-400}}{2\times 2}$$

Take the square root of -400.

$$x=\frac{0±20i}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±20i}{4}$$

Now solve the equation x=\frac{0±20i}{4} when ± is plus.

$$x=5i$$

Now solve the equation x=\frac{0±20i}{4} when ± is minus.

$$x=-5i$$

The equation is now solved.

$$x=5i x=-5i$$