Solve 14*x*3x+(1/2x)^2*3.14*2=32.97

$$14 \times x \times 3 x + ( \frac { 1 } { 2 } x ) ^ { 2 } \times 3.14 \times 2 = 32.97$$

Solve for x

$$x=\frac{\sqrt{14365029}}{4357}\approx 0.869892715$$

$$x=-\frac{\sqrt{14365029}}{4357}\approx -0.869892715$$

Steps by Finding Square Root

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

$$14x^{2}\times 3+\left(\frac{1}{2}x\right)^{2}\times 3.14\times 2=32.97$$

Multiply 14 and 3 to get 42.

$$42x^{2}+\left(\frac{1}{2}x\right)^{2}\times 3.14\times 2=32.97$$

Expand \left(\frac{1}{2}x\right)^{2}.

$$42x^{2}+\left(\frac{1}{2}\right)^{2}x^{2}\times 3.14\times 2=32.97$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$42x^{2}+\frac{1}{4}x^{2}\times 3.14\times 2=32.97$$

Multiply \frac{1}{4} and 3.14 to get \frac{157}{200}.

$$42x^{2}+\frac{157}{200}x^{2}\times 2=32.97$$

Multiply \frac{157}{200} and 2 to get \frac{157}{100}.

$$42x^{2}+\frac{157}{100}x^{2}=32.97$$

Combine 42x^{2} and \frac{157}{100}x^{2} to get \frac{4357}{100}x^{2}.

$$\frac{4357}{100}x^{2}=32.97$$

Multiply both sides by \frac{100}{4357}, the reciprocal of \frac{4357}{100}.

$$x^{2}=32.97\times \frac{100}{4357}$$

Multiply 32.97 and \frac{100}{4357} to get \frac{3297}{4357}.

$$x^{2}=\frac{3297}{4357}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{14365029}}{4357} x=-\frac{\sqrt{14365029}}{4357}$$

Steps Using the Quadratic Formula

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

$$14x^{2}\times 3+\left(\frac{1}{2}x\right)^{2}\times 3.14\times 2=32.97$$

Multiply 14 and 3 to get 42.

$$42x^{2}+\left(\frac{1}{2}x\right)^{2}\times 3.14\times 2=32.97$$

Expand \left(\frac{1}{2}x\right)^{2}.

$$42x^{2}+\left(\frac{1}{2}\right)^{2}x^{2}\times 3.14\times 2=32.97$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$42x^{2}+\frac{1}{4}x^{2}\times 3.14\times 2=32.97$$

Multiply \frac{1}{4} and 3.14 to get \frac{157}{200}.

$$42x^{2}+\frac{157}{200}x^{2}\times 2=32.97$$

Multiply \frac{157}{200} and 2 to get \frac{157}{100}.

$$42x^{2}+\frac{157}{100}x^{2}=32.97$$

Combine 42x^{2} and \frac{157}{100}x^{2} to get \frac{4357}{100}x^{2}.

$$\frac{4357}{100}x^{2}=32.97$$

Subtract 32.97 from both sides.

$$\frac{4357}{100}x^{2}-32.97=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{4357}{100} for a, 0 for b, and -32.97 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{4357}{100}\left(-32.97\right)}}{2\times \frac{4357}{100}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{4357}{100}\left(-32.97\right)}}{2\times \frac{4357}{100}}$$

Multiply -4 times \frac{4357}{100}.

$$x=\frac{0±\sqrt{-\frac{4357}{25}\left(-32.97\right)}}{2\times \frac{4357}{100}}$$

Multiply -\frac{4357}{25} times -32.97 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0±\sqrt{\frac{14365029}{2500}}}{2\times \frac{4357}{100}}$$

Take the square root of \frac{14365029}{2500}.

$$x=\frac{0±\frac{\sqrt{14365029}}{50}}{2\times \frac{4357}{100}}$$

Multiply 2 times \frac{4357}{100}.

$$x=\frac{0±\frac{\sqrt{14365029}}{50}}{\frac{4357}{50}}$$

Now solve the equation x=\frac{0±\frac{\sqrt{14365029}}{50}}{\frac{4357}{50}} when ± is plus.

$$x=\frac{\sqrt{14365029}}{4357}$$

Now solve the equation x=\frac{0±\frac{\sqrt{14365029}}{50}}{\frac{4357}{50}} when ± is minus.

$$x=-\frac{\sqrt{14365029}}{4357}$$

The equation is now solved.

$$x=\frac{\sqrt{14365029}}{4357} x=-\frac{\sqrt{14365029}}{4357}$$