Solve 4x^2+8=33xdiv4x

$$4 { x }^{ 2 } +8=33x \div 4x$$

Solve for x

$$x = \frac{4 \sqrt{34}}{17} \approx 1.371988681$$

$$x = -\frac{4 \sqrt{34}}{17} \approx -1.371988681$$

Steps by Finding Square Root

Multiply both sides of the equation by 4.

$$16x^{2}+32=33xx$$

Multiply x and x to get x^{2}.

$$16x^{2}+32=33x^{2}$$

Subtract 33x^{2} from both sides.

$$16x^{2}+32-33x^{2}=0$$

Combine 16x^{2} and -33x^{2} to get -17x^{2}.

$$-17x^{2}+32=0$$

Subtract 32 from both sides. Anything subtracted from zero gives its negation.

$$-17x^{2}=-32$$

Divide both sides by -17.

$$x^{2}=\frac{-32}{-17}$$

Fraction \frac{-32}{-17} can be simplified to \frac{32}{17} by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{32}{17}$$

Take the square root of both sides of the equation.

$$x=\frac{4\sqrt{34}}{17} x=-\frac{4\sqrt{34}}{17}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 4.

$$16x^{2}+32=33xx$$

Multiply x and x to get x^{2}.

$$16x^{2}+32=33x^{2}$$

Subtract 33x^{2} from both sides.

$$16x^{2}+32-33x^{2}=0$$

Combine 16x^{2} and -33x^{2} to get -17x^{2}.

$$-17x^{2}+32=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -17 for a, 0 for b, and 32 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-17\right)\times 32}}{2\left(-17\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-17\right)\times 32}}{2\left(-17\right)}$$

Multiply -4 times -17.

$$x=\frac{0±\sqrt{68\times 32}}{2\left(-17\right)}$$

Multiply 68 times 32.

$$x=\frac{0±\sqrt{2176}}{2\left(-17\right)}$$

Take the square root of 2176.

$$x=\frac{0±8\sqrt{34}}{2\left(-17\right)}$$

Multiply 2 times -17.

$$x=\frac{0±8\sqrt{34}}{-34}$$

Now solve the equation x=\frac{0±8\sqrt{34}}{-34} when ± is plus.

$$x=-\frac{4\sqrt{34}}{17}$$

Now solve the equation x=\frac{0±8\sqrt{34}}{-34} when ± is minus.

$$x=\frac{4\sqrt{34}}{17}$$

The equation is now solved.

$$x=-\frac{4\sqrt{34}}{17} x=\frac{4\sqrt{34}}{17}$$