Solve 185*10^6=143*400left(950-x^2/2right)

$$185 \times { 10 }^{ 6 } = 143 \cdot 400 \left( 950- \frac{ { x }^{ 2 } }{ 2 } \right)$$

Solve for x (complex solution)

$$x=-\frac{10\sqrt{934219}i}{143}\approx -0-67.590912618i$$

$$x=\frac{10\sqrt{934219}i}{143}\approx 67.590912618i$$

Steps by Finding Square Root

Multiply both sides of the equation by 2.

$$370\times 10^{6}=286\times 400\left(950-\frac{x^{2}}{2}\right)$$

Calculate 10 to the power of 6 and get 1000000.

$$370\times 1000000=286\times 400\left(950-\frac{x^{2}}{2}\right)$$

Multiply 370 and 1000000 to get 370000000.

$$370000000=286\times 400\left(950-\frac{x^{2}}{2}\right)$$

Multiply 286 and 400 to get 114400.

$$370000000=114400\left(950-\frac{x^{2}}{2}\right)$$

Use the distributive property to multiply 114400 by 950-\frac{x^{2}}{2}.

$$370000000=108680000+114400\left(-\frac{x^{2}}{2}\right)$$

Cancel out 2, the greatest common factor in 114400 and 2.

$$370000000=108680000-57200x^{2}$$

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

$$108680000-57200x^{2}=370000000$$

Subtract 108680000 from both sides.

$$-57200x^{2}=370000000-108680000$$

Subtract 108680000 from 370000000 to get 261320000.

$$-57200x^{2}=261320000$$

Divide both sides by -57200.

$$x^{2}=\frac{261320000}{-57200}$$

Reduce the fraction \frac{261320000}{-57200} to lowest terms by extracting and canceling out 400.

$$x^{2}=-\frac{653300}{143}$$

The equation is now solved.

$$x=\frac{10\sqrt{934219}i}{143} x=-\frac{10\sqrt{934219}i}{143}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 2.

$$370\times 10^{6}=286\times 400\left(950-\frac{x^{2}}{2}\right)$$

Calculate 10 to the power of 6 and get 1000000.

$$370\times 1000000=286\times 400\left(950-\frac{x^{2}}{2}\right)$$

Multiply 370 and 1000000 to get 370000000.

$$370000000=286\times 400\left(950-\frac{x^{2}}{2}\right)$$

Multiply 286 and 400 to get 114400.

$$370000000=114400\left(950-\frac{x^{2}}{2}\right)$$

Use the distributive property to multiply 114400 by 950-\frac{x^{2}}{2}.

$$370000000=108680000+114400\left(-\frac{x^{2}}{2}\right)$$

Cancel out 2, the greatest common factor in 114400 and 2.

$$370000000=108680000-57200x^{2}$$

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

$$108680000-57200x^{2}=370000000$$

Subtract 370000000 from both sides.

$$108680000-57200x^{2}-370000000=0$$

Subtract 370000000 from 108680000 to get -261320000.

$$-261320000-57200x^{2}=0$$

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.

$$-57200x^{2}-261320000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -57200 for a, 0 for b, and -261320000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-57200\right)\left(-261320000\right)}}{2\left(-57200\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-57200\right)\left(-261320000\right)}}{2\left(-57200\right)}$$

Multiply -4 times -57200.

$$x=\frac{0±\sqrt{228800\left(-261320000\right)}}{2\left(-57200\right)}$$

Multiply 228800 times -261320000.

$$x=\frac{0±\sqrt{-59790016000000}}{2\left(-57200\right)}$$

Take the square root of -59790016000000.

$$x=\frac{0±8000\sqrt{934219}i}{2\left(-57200\right)}$$

Multiply 2 times -57200.

$$x=\frac{0±8000\sqrt{934219}i}{-114400}$$

Now solve the equation x=\frac{0±8000\sqrt{934219}i}{-114400} when ± is plus.

$$x=-\frac{10\sqrt{934219}i}{143}$$

Now solve the equation x=\frac{0±8000\sqrt{934219}i}{-114400} when ± is minus.

$$x=\frac{10\sqrt{934219}i}{143}$$

The equation is now solved.

$$x=-\frac{10\sqrt{934219}i}{143} x=\frac{10\sqrt{934219}i}{143}$$