Solve (1+d^2=1+4d

$$( 1 + d ^ { 2 } = 1 + 4 d$$

Solve for d

$$d=4$$

$$d=0$$

Steps Using Factoring

Subtract 1 from both sides.

$$1+d^{2}-1=4d$$

Subtract 1 from 1 to get 0.

$$d^{2}=4d$$

Subtract 4d from both sides.

$$d^{2}-4d=0$$

Factor out d.

$$d\left(d-4\right)=0$$

To find equation solutions, solve d=0 and d-4=0.

$$d=0 d=4$$

Steps Using the Quadratic Formula

Subtract 1 from both sides.

$$1+d^{2}-1=4d$$

Subtract 1 from 1 to get 0.

$$d^{2}=4d$$

Subtract 4d from both sides.

$$d^{2}-4d=0$$

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

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

Take the square root of \left(-4\right)^{2}.

$$d=\frac{-\left(-4\right)±4}{2}$$

The opposite of -4 is 4.

$$d=\frac{4±4}{2}$$

Now solve the equation d=\frac{4±4}{2} when ± is plus. Add 4 to 4.

$$d=\frac{8}{2}$$

Divide 8 by 2.

$$d=4$$

Now solve the equation d=\frac{4±4}{2} when ± is minus. Subtract 4 from 4.

$$d=\frac{0}{2}$$

Divide 0 by 2.

$$d=0$$

The equation is now solved.

$$d=4 d=0$$

Steps for Completing the Square

Subtract 1 from both sides.

$$1+d^{2}-1=4d$$

Subtract 1 from 1 to get 0.

$$d^{2}=4d$$

Subtract 4d from both sides.

$$d^{2}-4d=0$$

Divide -4, the coefficient of the x term, by 2 to get -2. Then add the square of -2 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$d^{2}-4d+\left(-2\right)^{2}=\left(-2\right)^{2}$$

Square -2.

$$d^{2}-4d+4=4$$

Factor d^{2}-4d+4. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(d-2\right)^{2}=4$$

Take the square root of both sides of the equation.

$$\sqrt{\left(d-2\right)^{2}}=\sqrt{4}$$

Simplify.

$$d-2=2 d-2=-2$$

Add 2 to both sides of the equation.

$$d=4 d=0$$