Solve (5-2d)*5*(5+2d)=45

$$( 5 - 2 d ) \times 5 \times ( 5 + 2 d ) = 45$$

Solve for d

$$d=2$$

$$d=-2$$

Steps by Finding Square Root

Use the distributive property to multiply 5-2d by 5.

$$\left(25-10d\right)\left(5+2d\right)=45$$

Use the distributive property to multiply 25-10d by 5+2d and combine like terms.

$$125-20d^{2}=45$$

Subtract 125 from both sides.

$$-20d^{2}=45-125$$

Subtract 125 from 45 to get -80.

$$-20d^{2}=-80$$

Divide both sides by -20.

$$d^{2}=\frac{-80}{-20}$$

Divide -80 by -20 to get 4.

$$d^{2}=4$$

Take the square root of both sides of the equation.

$$d=2 d=-2$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 5-2d by 5.

$$\left(25-10d\right)\left(5+2d\right)=45$$

Use the distributive property to multiply 25-10d by 5+2d and combine like terms.

$$125-20d^{2}=45$$

Subtract 45 from both sides.

$$125-20d^{2}-45=0$$

Subtract 45 from 125 to get 80.

$$80-20d^{2}=0$$

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.

$$-20d^{2}+80=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -20 for a, 0 for b, and 80 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$d=\frac{0±\sqrt{0^{2}-4\left(-20\right)\times 80}}{2\left(-20\right)}$$

Square 0.

$$d=\frac{0±\sqrt{-4\left(-20\right)\times 80}}{2\left(-20\right)}$$

Multiply -4 times -20.

$$d=\frac{0±\sqrt{80\times 80}}{2\left(-20\right)}$$

Multiply 80 times 80.

$$d=\frac{0±\sqrt{6400}}{2\left(-20\right)}$$

Take the square root of 6400.

$$d=\frac{0±80}{2\left(-20\right)}$$

Multiply 2 times -20.

$$d=\frac{0±80}{-40}$$

Now solve the equation d=\frac{0±80}{-40} when ± is plus. Divide 80 by -40.

$$d=-2$$

Now solve the equation d=\frac{0±80}{-40} when ± is minus. Divide -80 by -40.

$$d=2$$

The equation is now solved.

$$d=-2 d=2$$