Solve 5x^2+3x^2=40

$$5 x ^ { 2 } + 3 x ^ { 2 } = 40$$

Solve for x

$$x=\sqrt{5}\approx 2.236067977$$

$$x=-\sqrt{5}\approx -2.236067977$$

Steps by Finding Square Root

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

$$8x^{2}=40$$

Divide both sides by 8.

$$x^{2}=\frac{40}{8}$$

Divide 40 by 8 to get 5.

$$x^{2}=5$$

Take the square root of both sides of the equation.

$$x=\sqrt{5} x=-\sqrt{5}$$

Steps Using the Quadratic Formula

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

$$8x^{2}=40$$

Subtract 40 from both sides.

$$8x^{2}-40=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 0 for b, and -40 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 8\left(-40\right)}}{2\times 8}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 8\left(-40\right)}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{0±\sqrt{-32\left(-40\right)}}{2\times 8}$$

Multiply -32 times -40.

$$x=\frac{0±\sqrt{1280}}{2\times 8}$$

Take the square root of 1280.

$$x=\frac{0±16\sqrt{5}}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{0±16\sqrt{5}}{16}$$

Now solve the equation x=\frac{0±16\sqrt{5}}{16} when ± is plus.

$$x=\sqrt{5}$$

Now solve the equation x=\frac{0±16\sqrt{5}}{16} when ± is minus.

$$x=-\sqrt{5}$$

The equation is now solved.

$$x=\sqrt{5} x=-\sqrt{5}$$