Solve 3d^2+5d^2=8

$$3 d ^ { 2 } + 5 d ^ { 2 } = 8$$

Solve for d

$$d=1$$

$$d=-1$$

Steps Using Difference of Squares

Combine 3d^{2} and 5d^{2} to get 8d^{2}.

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

Subtract 8 from both sides.

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

Divide both sides by 8.

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

Consider d^{2}-1. Rewrite d^{2}-1 as d^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(d-1\right)\left(d+1\right)=0$$

To find equation solutions, solve d-1=0 and d+1=0.

$$d=1 d=-1$$

Steps by Finding Square Root

Combine 3d^{2} and 5d^{2} to get 8d^{2}.

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

Divide both sides by 8.

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

Divide 8 by 8 to get 1.

$$d^{2}=1$$

Take the square root of both sides of the equation.

$$d=1 d=-1$$

Steps Using the Quadratic Formula

Combine 3d^{2} and 5d^{2} to get 8d^{2}.

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

Subtract 8 from both sides.

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

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

$$d=\frac{0±\sqrt{0^{2}-4\times 8\left(-8\right)}}{2\times 8}$$

Square 0.

$$d=\frac{0±\sqrt{-4\times 8\left(-8\right)}}{2\times 8}$$

Multiply -4 times 8.

$$d=\frac{0±\sqrt{-32\left(-8\right)}}{2\times 8}$$

Multiply -32 times -8.

$$d=\frac{0±\sqrt{256}}{2\times 8}$$

Take the square root of 256.

$$d=\frac{0±16}{2\times 8}$$

Multiply 2 times 8.

$$d=\frac{0±16}{16}$$

Now solve the equation d=\frac{0±16}{16} when ± is plus. Divide 16 by 16.

$$d=1$$

Now solve the equation d=\frac{0±16}{16} when ± is minus. Divide -16 by 16.

$$d=-1$$

The equation is now solved.

$$d=1 d=-1$$