Solve 3x^2+47x^2-7=0

$$3 x ^ { 2 } + 47 x ^ { 2 } - 7 = 0$$

Solve for x

$$x=\frac{\sqrt{14}}{10}\approx 0.374165739$$

$$x=-\frac{\sqrt{14}}{10}\approx -0.374165739$$

Steps by Finding Square Root

Combine 3x^{2} and 47x^{2} to get 50x^{2}.

$$50x^{2}-7=0$$

Add 7 to both sides. Anything plus zero gives itself.

$$50x^{2}=7$$

Divide both sides by 50.

$$x^{2}=\frac{7}{50}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{14}}{10} x=-\frac{\sqrt{14}}{10}$$

Steps Using the Quadratic Formula

Combine 3x^{2} and 47x^{2} to get 50x^{2}.

$$50x^{2}-7=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 50 for a, 0 for b, and -7 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 50\left(-7\right)}}{2\times 50}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 50\left(-7\right)}}{2\times 50}$$

Multiply -4 times 50.

$$x=\frac{0±\sqrt{-200\left(-7\right)}}{2\times 50}$$

Multiply -200 times -7.

$$x=\frac{0±\sqrt{1400}}{2\times 50}$$

Take the square root of 1400.

$$x=\frac{0±10\sqrt{14}}{2\times 50}$$

Multiply 2 times 50.

$$x=\frac{0±10\sqrt{14}}{100}$$

Now solve the equation x=\frac{0±10\sqrt{14}}{100} when ± is plus.

$$x=\frac{\sqrt{14}}{10}$$

Now solve the equation x=\frac{0±10\sqrt{14}}{100} when ± is minus.

$$x=-\frac{\sqrt{14}}{10}$$

The equation is now solved.

$$x=\frac{\sqrt{14}}{10} x=-\frac{\sqrt{14}}{10}$$