Solve 16x^2+10x^2=24

$$16 x ^ { 2 } + 10 x ^ { 2 } = 24$$

Solve for x

$$x=\frac{2\sqrt{39}}{13}\approx 0.960768923$$

$$x=-\frac{2\sqrt{39}}{13}\approx -0.960768923$$

Steps by Finding Square Root

Combine 16x^{2} and 10x^{2} to get 26x^{2}.

$$26x^{2}=24$$

Divide both sides by 26.

$$x^{2}=\frac{24}{26}$$

Reduce the fraction \frac{24}{26} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{12}{13}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{39}}{13} x=-\frac{2\sqrt{39}}{13}$$

Steps Using the Quadratic Formula

Combine 16x^{2} and 10x^{2} to get 26x^{2}.

$$26x^{2}=24$$

Subtract 24 from both sides.

$$26x^{2}-24=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 26 for a, 0 for b, and -24 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 26\left(-24\right)}}{2\times 26}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 26\left(-24\right)}}{2\times 26}$$

Multiply -4 times 26.

$$x=\frac{0±\sqrt{-104\left(-24\right)}}{2\times 26}$$

Multiply -104 times -24.

$$x=\frac{0±\sqrt{2496}}{2\times 26}$$

Take the square root of 2496.

$$x=\frac{0±8\sqrt{39}}{2\times 26}$$

Multiply 2 times 26.

$$x=\frac{0±8\sqrt{39}}{52}$$

Now solve the equation x=\frac{0±8\sqrt{39}}{52} when ± is plus.

$$x=\frac{2\sqrt{39}}{13}$$

Now solve the equation x=\frac{0±8\sqrt{39}}{52} when ± is minus.

$$x=-\frac{2\sqrt{39}}{13}$$

The equation is now solved.

$$x=\frac{2\sqrt{39}}{13} x=-\frac{2\sqrt{39}}{13}$$