Solve -1(1-d^2)=8

$$- 1 ( 1 - d ^ { 2 } ) = 8$$

Solve for d

$$d=3$$

$$d=-3$$

Steps by Finding Square Root

Divide both sides by -1.

$$1-d^{2}=-8$$

Subtract 1 from both sides.

$$-d^{2}=-8-1$$

Subtract 1 from -8 to get -9.

$$-d^{2}=-9$$

Divide both sides by -1.

$$d^{2}=\frac{-9}{-1}$$

Fraction \frac{-9}{-1} can be simplified to 9 by removing the negative sign from both the numerator and the denominator.

$$d^{2}=9$$

Take the square root of both sides of the equation.

$$d=3 d=-3$$

Steps Using the Quadratic Formula

Divide both sides by -1.

$$1-d^{2}=-8$$

Add 8 to both sides.

$$1-d^{2}+8=0$$

Add 1 and 8 to get 9.

$$9-d^{2}=0$$

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.

$$-d^{2}+9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$d=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 9}}{2\left(-1\right)}$$

Square 0.

$$d=\frac{0±\sqrt{-4\left(-1\right)\times 9}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$d=\frac{0±\sqrt{4\times 9}}{2\left(-1\right)}$$

Multiply 4 times 9.

$$d=\frac{0±\sqrt{36}}{2\left(-1\right)}$$

Take the square root of 36.

$$d=\frac{0±6}{2\left(-1\right)}$$

Multiply 2 times -1.

$$d=\frac{0±6}{-2}$$

Now solve the equation d=\frac{0±6}{-2} when ± is plus. Divide 6 by -2.

$$d=-3$$

Now solve the equation d=\frac{0±6}{-2} when ± is minus. Divide -6 by -2.

$$d=3$$

The equation is now solved.

$$d=-3 d=3$$