Solve 1/2*(14000+8600)*3.615^2+1/2*(0.32*10^6)*x^2=0

$$\frac { 1 } { 2 } \cdot ( 14000 + 8600 ) \cdot 3.615 ^ { 2 } + \frac { 1 } { 2 } \cdot ( 0.32 \cdot 10 ^ { 6 } ) \cdot x ^ { 2 } = 0$$

Solve for x (complex solution)

$$x=-\frac{i\times 723\sqrt{113}}{8000}\approx -0-0.960699428i$$

$$x=\frac{i\times 723\sqrt{113}}{8000}\approx 0.960699428i$$

Steps by Finding Square Root

Add 14000 and 8600 to get 22600.

$$\frac{1}{2}\times 22600\times 3.615^{2}+\frac{1}{2}\times 0.32\times 10^{6}x^{2}=0$$

Multiply \frac{1}{2} and 22600 to get 11300.

$$11300\times 3.615^{2}+\frac{1}{2}\times 0.32\times 10^{6}x^{2}=0$$

Calculate 3.615 to the power of 2 and get 13.068225.

$$11300\times 13.068225+\frac{1}{2}\times 0.32\times 10^{6}x^{2}=0$$

Multiply 11300 and 13.068225 to get 147670.9425.

$$147670.9425+\frac{1}{2}\times 0.32\times 10^{6}x^{2}=0$$

Multiply \frac{1}{2} and 0.32 to get \frac{4}{25}.

$$147670.9425+\frac{4}{25}\times 10^{6}x^{2}=0$$

Calculate 10 to the power of 6 and get 1000000.

$$147670.9425+\frac{4}{25}\times 1000000x^{2}=0$$

Multiply \frac{4}{25} and 1000000 to get 160000.

$$147670.9425+160000x^{2}=0$$

Subtract 147670.9425 from both sides. Anything subtracted from zero gives its negation.

$$160000x^{2}=-147670.9425$$

Divide both sides by 160000.

$$x^{2}=\frac{-147670.9425}{160000}$$

Expand \frac{-147670.9425}{160000} by multiplying both numerator and the denominator by 10000.

$$x^{2}=\frac{-1476709425}{1600000000}$$

Reduce the fraction \frac{-1476709425}{1600000000} to lowest terms by extracting and canceling out 25.

$$x^{2}=-\frac{59068377}{64000000}$$

The equation is now solved.

$$x=\frac{723\sqrt{113}i}{8000} x=-\frac{723\sqrt{113}i}{8000}$$

Steps Using the Quadratic Formula

Add 14000 and 8600 to get 22600.

$$\frac{1}{2}\times 22600\times 3.615^{2}+\frac{1}{2}\times 0.32\times 10^{6}x^{2}=0$$

Multiply \frac{1}{2} and 22600 to get 11300.

$$11300\times 3.615^{2}+\frac{1}{2}\times 0.32\times 10^{6}x^{2}=0$$

Calculate 3.615 to the power of 2 and get 13.068225.

$$11300\times 13.068225+\frac{1}{2}\times 0.32\times 10^{6}x^{2}=0$$

Multiply 11300 and 13.068225 to get 147670.9425.

$$147670.9425+\frac{1}{2}\times 0.32\times 10^{6}x^{2}=0$$

Multiply \frac{1}{2} and 0.32 to get \frac{4}{25}.

$$147670.9425+\frac{4}{25}\times 10^{6}x^{2}=0$$

Calculate 10 to the power of 6 and get 1000000.

$$147670.9425+\frac{4}{25}\times 1000000x^{2}=0$$

Multiply \frac{4}{25} and 1000000 to get 160000.

$$147670.9425+160000x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$160000x^{2}+147670.9425=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 160000 for a, 0 for b, and 147670.9425 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 160000\times 147670.9425}}{2\times 160000}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 160000\times 147670.9425}}{2\times 160000}$$

Multiply -4 times 160000.

$$x=\frac{0±\sqrt{-640000\times 147670.9425}}{2\times 160000}$$

Multiply -640000 times 147670.9425.

$$x=\frac{0±\sqrt{-94509403200}}{2\times 160000}$$

Take the square root of -94509403200.

$$x=\frac{0±28920\sqrt{113}i}{2\times 160000}$$

Multiply 2 times 160000.

$$x=\frac{0±28920\sqrt{113}i}{320000}$$

Now solve the equation x=\frac{0±28920\sqrt{113}i}{320000} when ± is plus.

$$x=\frac{723\sqrt{113}i}{8000}$$

Now solve the equation x=\frac{0±28920\sqrt{113}i}{320000} when ± is minus.

$$x=-\frac{723\sqrt{113}i}{8000}$$

The equation is now solved.

$$x=\frac{723\sqrt{113}i}{8000} x=-\frac{723\sqrt{113}i}{8000}$$