Solve -x^2-5=-35-4x^2

$$- x ^ { 2 } - 5 = - 35 - 4 x ^ { 2 }$$

Solve for x (complex solution)

$$x=-\sqrt{10}i\approx -0-3.16227766i$$

$$x=\sqrt{10}i\approx 3.16227766i$$

Steps by Finding Square Root

Add 4x^{2} to both sides.

$$-x^{2}-5+4x^{2}=-35$$

Add 5 to both sides.

$$-x^{2}+4x^{2}=-35+5$$

Add -35 and 5 to get -30.

$$-x^{2}+4x^{2}=-30$$

Combine -x^{2} and 4x^{2} to get 3x^{2}.

$$3x^{2}=-30$$

Divide both sides by 3.

$$x^{2}=\frac{-30}{3}$$

Divide -30 by 3 to get -10.

$$x^{2}=-10$$

The equation is now solved.

$$x=\sqrt{10}i x=-\sqrt{10}i$$

Steps Using the Quadratic Formula

Subtract -35 from both sides.

$$-x^{2}-5-\left(-35\right)=-4x^{2}$$

The opposite of -35 is 35.

$$-x^{2}-5+35=-4x^{2}$$

Add 4x^{2} to both sides.

$$-x^{2}-5+35+4x^{2}=0$$

Add -5 and 35 to get 30.

$$-x^{2}+30+4x^{2}=0$$

Combine -x^{2} and 4x^{2} to get 3x^{2}.

$$3x^{2}+30=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and 30 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\times 30}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\times 30}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\times 30}}{2\times 3}$$

Multiply -12 times 30.

$$x=\frac{0±\sqrt{-360}}{2\times 3}$$

Take the square root of -360.

$$x=\frac{0±6\sqrt{10}i}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±6\sqrt{10}i}{6}$$

Now solve the equation x=\frac{0±6\sqrt{10}i}{6} when ± is plus.

$$x=\sqrt{10}i$$

Now solve the equation x=\frac{0±6\sqrt{10}i}{6} when ± is minus.

$$x=-\sqrt{10}i$$

The equation is now solved.

$$x=\sqrt{10}i x=-\sqrt{10}i$$