Solve 8x^2=15(18-44)

$$8 x ^ { 2 } = 15 ( 18 - 44 )$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{195}i}{2}\approx -0-6.982120022i$$

$$x=\frac{\sqrt{195}i}{2}\approx 6.982120022i$$

Steps by Finding Square Root

Subtract 44 from 18 to get -26.

$$8x^{2}=15\left(-26\right)$$

Multiply 15 and -26 to get -390.

$$8x^{2}=-390$$

Divide both sides by 8.

$$x^{2}=\frac{-390}{8}$$

Reduce the fraction \frac{-390}{8} to lowest terms by extracting and canceling out 2.

$$x^{2}=-\frac{195}{4}$$

The equation is now solved.

$$x=\frac{\sqrt{195}i}{2} x=-\frac{\sqrt{195}i}{2}$$

Steps Using the Quadratic Formula

Subtract 44 from 18 to get -26.

$$8x^{2}=15\left(-26\right)$$

Multiply 15 and -26 to get -390.

$$8x^{2}=-390$$

Add 390 to both sides.

$$8x^{2}+390=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 0 for b, and 390 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 8\times 390}}{2\times 8}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 8\times 390}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{0±\sqrt{-32\times 390}}{2\times 8}$$

Multiply -32 times 390.

$$x=\frac{0±\sqrt{-12480}}{2\times 8}$$

Take the square root of -12480.

$$x=\frac{0±8\sqrt{195}i}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{0±8\sqrt{195}i}{16}$$

Now solve the equation x=\frac{0±8\sqrt{195}i}{16} when ± is plus.

$$x=\frac{\sqrt{195}i}{2}$$

Now solve the equation x=\frac{0±8\sqrt{195}i}{16} when ± is minus.

$$x=-\frac{\sqrt{195}i}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{195}i}{2} x=-\frac{\sqrt{195}i}{2}$$