Solve 185*10^6=14.3*400left(950-x^2/2right)

$$185 \times { 10 }^{ 6 } = 14.3 \cdot 400 \left( 950- \frac{ { x }^{ 2 } }{ 2 } \right)$$

Solve for x (complex solution)

$$x=-\frac{i\times 10\sqrt{12838969}}{143}\approx -0-250.569979617i$$

$$x=\frac{i\times 10\sqrt{12838969}}{143}\approx 250.569979617i$$

Steps by Finding Square Root

Multiply both sides of the equation by 2.

$$370\times 10^{6}=28.6\times 400\left(950-\frac{x^{2}}{2}\right)$$

Calculate 10 to the power of 6 and get 1000000.

$$370\times 1000000=28.6\times 400\left(950-\frac{x^{2}}{2}\right)$$

Multiply 370 and 1000000 to get 370000000.

$$370000000=28.6\times 400\left(950-\frac{x^{2}}{2}\right)$$

Multiply 28.6 and 400 to get 11440.

$$370000000=11440\left(950-\frac{x^{2}}{2}\right)$$

Use the distributive property to multiply 11440 by 950-\frac{x^{2}}{2}.

$$370000000=10868000+11440\left(-\frac{x^{2}}{2}\right)$$

Cancel out 2, the greatest common factor in 11440 and 2.

$$370000000=10868000-5720x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$10868000-5720x^{2}=370000000$$

Subtract 10868000 from both sides.

$$-5720x^{2}=370000000-10868000$$

Subtract 10868000 from 370000000 to get 359132000.

$$-5720x^{2}=359132000$$

Divide both sides by -5720.

$$x^{2}=\frac{359132000}{-5720}$$

Reduce the fraction \frac{359132000}{-5720} to lowest terms by extracting and canceling out 40.

$$x^{2}=-\frac{8978300}{143}$$

The equation is now solved.

$$x=\frac{10\sqrt{12838969}i}{143} x=-\frac{10\sqrt{12838969}i}{143}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 2.

$$370\times 10^{6}=28.6\times 400\left(950-\frac{x^{2}}{2}\right)$$

Calculate 10 to the power of 6 and get 1000000.

$$370\times 1000000=28.6\times 400\left(950-\frac{x^{2}}{2}\right)$$

Multiply 370 and 1000000 to get 370000000.

$$370000000=28.6\times 400\left(950-\frac{x^{2}}{2}\right)$$

Multiply 28.6 and 400 to get 11440.

$$370000000=11440\left(950-\frac{x^{2}}{2}\right)$$

Use the distributive property to multiply 11440 by 950-\frac{x^{2}}{2}.

$$370000000=10868000+11440\left(-\frac{x^{2}}{2}\right)$$

Cancel out 2, the greatest common factor in 11440 and 2.

$$370000000=10868000-5720x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$10868000-5720x^{2}=370000000$$

Subtract 370000000 from both sides.

$$10868000-5720x^{2}-370000000=0$$

Subtract 370000000 from 10868000 to get -359132000.

$$-359132000-5720x^{2}=0$$

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.

$$-5720x^{2}-359132000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -5720 for a, 0 for b, and -359132000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-5720\right)\left(-359132000\right)}}{2\left(-5720\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-5720\right)\left(-359132000\right)}}{2\left(-5720\right)}$$

Multiply -4 times -5720.

$$x=\frac{0±\sqrt{22880\left(-359132000\right)}}{2\left(-5720\right)}$$

Multiply 22880 times -359132000.

$$x=\frac{0±\sqrt{-8216940160000}}{2\left(-5720\right)}$$

Take the square root of -8216940160000.

$$x=\frac{0±800\sqrt{12838969}i}{2\left(-5720\right)}$$

Multiply 2 times -5720.

$$x=\frac{0±800\sqrt{12838969}i}{-11440}$$

Now solve the equation x=\frac{0±800\sqrt{12838969}i}{-11440} when ± is plus.

$$x=-\frac{10\sqrt{12838969}i}{143}$$

Now solve the equation x=\frac{0±800\sqrt{12838969}i}{-11440} when ± is minus.

$$x=\frac{10\sqrt{12838969}i}{143}$$

The equation is now solved.

$$x=-\frac{10\sqrt{12838969}i}{143} x=\frac{10\sqrt{12838969}i}{143}$$