Solve 4t^2+1=0

$$4 t ^ { 2 } + 1 = 0$$

Solve for t

$$t=-\frac{1}{2}i=-0.5i$$

$$t=\frac{1}{2}i=0.5i$$

Steps by Finding Square Root

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

$$4t^{2}=-1$$

Divide both sides by 4.

$$t^{2}=-\frac{1}{4}$$

The equation is now solved.

$$t=\frac{1}{2}i t=-\frac{1}{2}i$$

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.

$$4t^{2}+1=0$$

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

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

Square 0.

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

Multiply -4 times 4.

$$t=\frac{0±\sqrt{-16}}{2\times 4}$$

Take the square root of -16.

$$t=\frac{0±4i}{2\times 4}$$

Multiply 2 times 4.

$$t=\frac{0±4i}{8}$$

Now solve the equation t=\frac{0±4i}{8} when ± is plus.

$$t=\frac{1}{2}i$$

Now solve the equation t=\frac{0±4i}{8} when ± is minus.

$$t=-\frac{1}{2}i$$

The equation is now solved.

$$t=\frac{1}{2}i t=-\frac{1}{2}i$$