Solve 2*14x^2+121x^2=9

$$2 \times 14 { x }^{ 2 } +121 { x }^{ 2 } =9$$

Solve for x

$$x=\frac{3\sqrt{149}}{149}\approx 0.245769576$$

$$x=-\frac{3\sqrt{149}}{149}\approx -0.245769576$$

Steps by Finding Square Root

Multiply 2 and 14 to get 28.

$$28x^{2}+121x^{2}=9$$

Combine 28x^{2} and 121x^{2} to get 149x^{2}.

$$149x^{2}=9$$

Divide both sides by 149.

$$x^{2}=\frac{9}{149}$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{149}}{149} x=-\frac{3\sqrt{149}}{149}$$

Steps Using the Quadratic Formula

Multiply 2 and 14 to get 28.

$$28x^{2}+121x^{2}=9$$

Combine 28x^{2} and 121x^{2} to get 149x^{2}.

$$149x^{2}=9$$

Subtract 9 from both sides.

$$149x^{2}-9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 149 for a, 0 for b, and -9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 149\left(-9\right)}}{2\times 149}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 149\left(-9\right)}}{2\times 149}$$

Multiply -4 times 149.

$$x=\frac{0±\sqrt{-596\left(-9\right)}}{2\times 149}$$

Multiply -596 times -9.

$$x=\frac{0±\sqrt{5364}}{2\times 149}$$

Take the square root of 5364.

$$x=\frac{0±6\sqrt{149}}{2\times 149}$$

Multiply 2 times 149.

$$x=\frac{0±6\sqrt{149}}{298}$$

Now solve the equation x=\frac{0±6\sqrt{149}}{298} when ± is plus.

$$x=\frac{3\sqrt{149}}{149}$$

Now solve the equation x=\frac{0±6\sqrt{149}}{298} when ± is minus.

$$x=-\frac{3\sqrt{149}}{149}$$

The equation is now solved.

$$x=\frac{3\sqrt{149}}{149} x=-\frac{3\sqrt{149}}{149}$$