Solve 3x^2+x^2-1900=0

$$3 { x }^{ 2 } + { x }^{ 2 } -1900=0$$

Solve for x

$$x=5\sqrt{19}\approx 21.794494718$$

$$x=-5\sqrt{19}\approx -21.794494718$$

Steps by Finding Square Root

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

$$4x^{2}-1900=0$$

Add 1900 to both sides. Anything plus zero gives itself.

$$4x^{2}=1900$$

Divide both sides by 4.

$$x^{2}=\frac{1900}{4}$$

Divide 1900 by 4 to get 475.

$$x^{2}=475$$

Take the square root of both sides of the equation.

$$x=5\sqrt{19} x=-5\sqrt{19}$$

Steps Using the Quadratic Formula

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

$$4x^{2}-1900=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -1900 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-1900\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-1900\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-1900\right)}}{2\times 4}$$

Multiply -16 times -1900.

$$x=\frac{0±\sqrt{30400}}{2\times 4}$$

Take the square root of 30400.

$$x=\frac{0±40\sqrt{19}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±40\sqrt{19}}{8}$$

Now solve the equation x=\frac{0±40\sqrt{19}}{8} when ± is plus.

$$x=5\sqrt{19}$$

Now solve the equation x=\frac{0±40\sqrt{19}}{8} when ± is minus.

$$x=-5\sqrt{19}$$

The equation is now solved.

$$x=5\sqrt{19} x=-5\sqrt{19}$$