Solve 7t^2+1=0

$$7 t ^ { 2 } + 1 = 0$$

Solve for t

$$t=-\frac{\sqrt{7}i}{7}\approx -0-0.377964473i$$

$$t=\frac{\sqrt{7}i}{7}\approx 0.377964473i$$

Steps by Finding Square Root

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$7t^{2}=-1$$

Divide both sides by 7.

$$t^{2}=-\frac{1}{7}$$

The equation is now solved.

$$t=\frac{\sqrt{7}i}{7} t=-\frac{\sqrt{7}i}{7}$$

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.

$$7t^{2}+1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, 0 for b, and 1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\times 7}}{2\times 7}$$

Square 0.

$$t=\frac{0±\sqrt{-4\times 7}}{2\times 7}$$

Multiply -4 times 7.

$$t=\frac{0±\sqrt{-28}}{2\times 7}$$

Take the square root of -28.

$$t=\frac{0±2\sqrt{7}i}{2\times 7}$$

Multiply 2 times 7.

$$t=\frac{0±2\sqrt{7}i}{14}$$

Now solve the equation t=\frac{0±2\sqrt{7}i}{14} when ± is plus.

$$t=\frac{\sqrt{7}i}{7}$$

Now solve the equation t=\frac{0±2\sqrt{7}i}{14} when ± is minus.

$$t=-\frac{\sqrt{7}i}{7}$$

The equation is now solved.

$$t=\frac{\sqrt{7}i}{7} t=-\frac{\sqrt{7}i}{7}$$