Solve 700^2+850^2=600^2-950x^2

$${ 700 }^{ 2 } + { 850 }^{ 2 } = { 600 }^{ 2 } -950 { x }^{ 2 }$$

Solve for x (complex solution)

$$x=-\frac{5\sqrt{12958}i}{19}\approx -0-29.956108243i$$

$$x=\frac{5\sqrt{12958}i}{19}\approx 29.956108243i$$

Steps by Finding Square Root

Calculate 700 to the power of 2 and get 490000.

$$490000+850^{2}=600^{2}-950x^{2}$$

Calculate 850 to the power of 2 and get 722500.

$$490000+722500=600^{2}-950x^{2}$$

Add 490000 and 722500 to get 1212500.

$$1212500=600^{2}-950x^{2}$$

Calculate 600 to the power of 2 and get 360000.

$$1212500=360000-950x^{2}$$

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

$$360000-950x^{2}=1212500$$

Subtract 360000 from both sides.

$$-950x^{2}=1212500-360000$$

Subtract 360000 from 1212500 to get 852500.

$$-950x^{2}=852500$$

Divide both sides by -950.

$$x^{2}=\frac{852500}{-950}$$

Reduce the fraction \frac{852500}{-950} to lowest terms by extracting and canceling out 50.

$$x^{2}=-\frac{17050}{19}$$

The equation is now solved.

$$x=\frac{5\sqrt{12958}i}{19} x=-\frac{5\sqrt{12958}i}{19}$$

Steps Using the Quadratic Formula

Calculate 700 to the power of 2 and get 490000.

$$490000+850^{2}=600^{2}-950x^{2}$$

Calculate 850 to the power of 2 and get 722500.

$$490000+722500=600^{2}-950x^{2}$$

Add 490000 and 722500 to get 1212500.

$$1212500=600^{2}-950x^{2}$$

Calculate 600 to the power of 2 and get 360000.

$$1212500=360000-950x^{2}$$

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

$$360000-950x^{2}=1212500$$

Subtract 1212500 from both sides.

$$360000-950x^{2}-1212500=0$$

Subtract 1212500 from 360000 to get -852500.

$$-852500-950x^{2}=0$$

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.

$$-950x^{2}-852500=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -950 for a, 0 for b, and -852500 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-950\right)\left(-852500\right)}}{2\left(-950\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-950\right)\left(-852500\right)}}{2\left(-950\right)}$$

Multiply -4 times -950.

$$x=\frac{0±\sqrt{3800\left(-852500\right)}}{2\left(-950\right)}$$

Multiply 3800 times -852500.

$$x=\frac{0±\sqrt{-3239500000}}{2\left(-950\right)}$$

Take the square root of -3239500000.

$$x=\frac{0±500\sqrt{12958}i}{2\left(-950\right)}$$

Multiply 2 times -950.

$$x=\frac{0±500\sqrt{12958}i}{-1900}$$

Now solve the equation x=\frac{0±500\sqrt{12958}i}{-1900} when ± is plus.

$$x=-\frac{5\sqrt{12958}i}{19}$$

Now solve the equation x=\frac{0±500\sqrt{12958}i}{-1900} when ± is minus.

$$x=\frac{5\sqrt{12958}i}{19}$$

The equation is now solved.

$$x=-\frac{5\sqrt{12958}i}{19} x=\frac{5\sqrt{12958}i}{19}$$