Solve (x^2+5)*17/25=34

$$\frac { ( x ^ { 2 } + 5 ) \times 17 } { 25 } = 34$$

Solve for x

$$x=3\sqrt{5}\approx 6.708203932$$

$$x=-3\sqrt{5}\approx -6.708203932$$

Steps by Finding Square Root

Multiply both sides by 25.

$$\left(x^{2}+5\right)\times 17=34\times 25$$

Use the distributive property to multiply x^{2}+5 by 17.

$$17x^{2}+85=34\times 25$$

Multiply 34 and 25 to get 850.

$$17x^{2}+85=850$$

Subtract 85 from both sides.

$$17x^{2}=850-85$$

Subtract 85 from 850 to get 765.

$$17x^{2}=765$$

Divide both sides by 17.

$$x^{2}=\frac{765}{17}$$

Divide 765 by 17 to get 45.

$$x^{2}=45$$

Take the square root of both sides of the equation.

$$x=3\sqrt{5} x=-3\sqrt{5}$$

Steps Using the Quadratic Formula

Multiply both sides by 25.

$$\left(x^{2}+5\right)\times 17=34\times 25$$

Use the distributive property to multiply x^{2}+5 by 17.

$$17x^{2}+85=34\times 25$$

Multiply 34 and 25 to get 850.

$$17x^{2}+85=850$$

Subtract 850 from both sides.

$$17x^{2}+85-850=0$$

Subtract 850 from 85 to get -765.

$$17x^{2}-765=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 17 for a, 0 for b, and -765 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 17\left(-765\right)}}{2\times 17}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 17\left(-765\right)}}{2\times 17}$$

Multiply -4 times 17.

$$x=\frac{0±\sqrt{-68\left(-765\right)}}{2\times 17}$$

Multiply -68 times -765.

$$x=\frac{0±\sqrt{52020}}{2\times 17}$$

Take the square root of 52020.

$$x=\frac{0±102\sqrt{5}}{2\times 17}$$

Multiply 2 times 17.

$$x=\frac{0±102\sqrt{5}}{34}$$

Now solve the equation x=\frac{0±102\sqrt{5}}{34} when ± is plus.

$$x=3\sqrt{5}$$

Now solve the equation x=\frac{0±102\sqrt{5}}{34} when ± is minus.

$$x=-3\sqrt{5}$$

The equation is now solved.

$$x=3\sqrt{5} x=-3\sqrt{5}$$