Solve 4x^2-35+69=0

$$4 { x }^{ 2 } -35+69=0$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{34}i}{2}\approx -0-2.915475947i$$

$$x=\frac{\sqrt{34}i}{2}\approx 2.915475947i$$

Steps by Finding Square Root

Add -35 and 69 to get 34.

$$4x^{2}+34=0$$

Subtract 34 from both sides. Anything subtracted from zero gives its negation.

$$4x^{2}=-34$$

Divide both sides by 4.

$$x^{2}=\frac{-34}{4}$$

Reduce the fraction \frac{-34}{4} to lowest terms by extracting and canceling out 2.

$$x^{2}=-\frac{17}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{34}i}{2} x=-\frac{\sqrt{34}i}{2}$$

Steps Using the Quadratic Formula

Add -35 and 69 to get 34.

$$4x^{2}+34=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and 34 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\times 34}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\times 34}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\times 34}}{2\times 4}$$

Multiply -16 times 34.

$$x=\frac{0±\sqrt{-544}}{2\times 4}$$

Take the square root of -544.

$$x=\frac{0±4\sqrt{34}i}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±4\sqrt{34}i}{8}$$

Now solve the equation x=\frac{0±4\sqrt{34}i}{8} when ± is plus.

$$x=\frac{\sqrt{34}i}{2}$$

Now solve the equation x=\frac{0±4\sqrt{34}i}{8} when ± is minus.

$$x=-\frac{\sqrt{34}i}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{34}i}{2} x=-\frac{\sqrt{34}i}{2}$$