Solve 76*84=(-x^2+1)

$$76 \cdot 84 = ( - x ^ { 2 } + 1 )$$

Solve for x (complex solution)

$$x=-\sqrt{6383}i\approx -0-79.893679349i$$

$$x=\sqrt{6383}i\approx 79.893679349i$$

Steps by Finding Square Root

Multiply 76 and 84 to get 6384.

$$6384=-x^{2}+1$$

Swap sides so that all variable terms are on the left hand side.

$$-x^{2}+1=6384$$

Subtract 1 from both sides.

$$-x^{2}=6384-1$$

Subtract 1 from 6384 to get 6383.

$$-x^{2}=6383$$

Divide both sides by -1.

$$x^{2}=-6383$$

The equation is now solved.

$$x=\sqrt{6383}i x=-\sqrt{6383}i$$

Steps Using the Quadratic Formula

Multiply 76 and 84 to get 6384.

$$6384=-x^{2}+1$$

Swap sides so that all variable terms are on the left hand side.

$$-x^{2}+1=6384$$

Subtract 6384 from both sides.

$$-x^{2}+1-6384=0$$

Subtract 6384 from 1 to get -6383.

$$-x^{2}-6383=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and -6383 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\left(-6383\right)}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\left(-6383\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\left(-6383\right)}}{2\left(-1\right)}$$

Multiply 4 times -6383.

$$x=\frac{0±\sqrt{-25532}}{2\left(-1\right)}$$

Take the square root of -25532.

$$x=\frac{0±2\sqrt{6383}i}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±2\sqrt{6383}i}{-2}$$

Now solve the equation x=\frac{0±2\sqrt{6383}i}{-2} when ± is plus.

$$x=-\sqrt{6383}i$$

Now solve the equation x=\frac{0±2\sqrt{6383}i}{-2} when ± is minus.

$$x=\sqrt{6383}i$$

The equation is now solved.

$$x=-\sqrt{6383}i x=\sqrt{6383}i$$