Solve 2(4/3)x^2=14(54)-23-5^2

$$2( \frac{ 4 }{ 3 } ) { x }^{ 2 } =14(54)-23- { 5 }^{ 2 }$$

Solve for x

$$x = \frac{3 \sqrt{118}}{2} \approx 16.294170737$$

$$x = -\frac{3 \sqrt{118}}{2} \approx -16.294170737$$

Steps by Finding Square Root

Multiply 2 and \frac{4}{3} to get \frac{8}{3}.

$$\frac{8}{3}x^{2}=14\times 54-23-5^{2}$$

Multiply 14 and 54 to get 756.

$$\frac{8}{3}x^{2}=756-23-5^{2}$$

Subtract 23 from 756 to get 733.

$$\frac{8}{3}x^{2}=733-5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{8}{3}x^{2}=733-25$$

Subtract 25 from 733 to get 708.

$$\frac{8}{3}x^{2}=708$$

Multiply both sides by \frac{3}{8}, the reciprocal of \frac{8}{3}.

$$x^{2}=708\times \frac{3}{8}$$

Multiply 708 and \frac{3}{8} to get \frac{531}{2}.

$$x^{2}=\frac{531}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{118}}{2} x=-\frac{3\sqrt{118}}{2}$$

Steps Using the Quadratic Formula

Multiply 2 and \frac{4}{3} to get \frac{8}{3}.

$$\frac{8}{3}x^{2}=14\times 54-23-5^{2}$$

Multiply 14 and 54 to get 756.

$$\frac{8}{3}x^{2}=756-23-5^{2}$$

Subtract 23 from 756 to get 733.

$$\frac{8}{3}x^{2}=733-5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{8}{3}x^{2}=733-25$$

Subtract 25 from 733 to get 708.

$$\frac{8}{3}x^{2}=708$$

Subtract 708 from both sides.

$$\frac{8}{3}x^{2}-708=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{8}{3} for a, 0 for b, and -708 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{8}{3}\left(-708\right)}}{2\times \frac{8}{3}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{8}{3}\left(-708\right)}}{2\times \frac{8}{3}}$$

Multiply -4 times \frac{8}{3}.

$$x=\frac{0±\sqrt{-\frac{32}{3}\left(-708\right)}}{2\times \frac{8}{3}}$$

Multiply -\frac{32}{3} times -708.

$$x=\frac{0±\sqrt{7552}}{2\times \frac{8}{3}}$$

Take the square root of 7552.

$$x=\frac{0±8\sqrt{118}}{2\times \frac{8}{3}}$$

Multiply 2 times \frac{8}{3}.

$$x=\frac{0±8\sqrt{118}}{\frac{16}{3}}$$

Now solve the equation x=\frac{0±8\sqrt{118}}{\frac{16}{3}} when ± is plus.

$$x=\frac{3\sqrt{118}}{2}$$

Now solve the equation x=\frac{0±8\sqrt{118}}{\frac{16}{3}} when ± is minus.

$$x=-\frac{3\sqrt{118}}{2}$$

The equation is now solved.

$$x=\frac{3\sqrt{118}}{2} x=-\frac{3\sqrt{118}}{2}$$