Solve 3x^2+4x^2=7

$$3 x ^ { 2 } + 4 x ^ { 2 } = 7$$

Solve for x

$$x=1$$

$$x=-1$$

Steps Using Difference of Squares

Combine 3x^{2} and 4x^{2} to get 7x^{2}.

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

Subtract 7 from both sides.

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

Divide both sides by 7.

$$x^{2}-1=0$$

Consider x^{2}-1. Rewrite x^{2}-1 as x^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-1\right)\left(x+1\right)=0$$

To find equation solutions, solve x-1=0 and x+1=0.

$$x=1 x=-1$$

Steps by Finding Square Root

Combine 3x^{2} and 4x^{2} to get 7x^{2}.

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

Divide both sides by 7.

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

Divide 7 by 7 to get 1.

$$x^{2}=1$$

Take the square root of both sides of the equation.

$$x=1 x=-1$$

Steps Using the Quadratic Formula

Combine 3x^{2} and 4x^{2} to get 7x^{2}.

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

Subtract 7 from both sides.

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

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

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

Square 0.

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

Multiply -4 times 7.

$$x=\frac{0±\sqrt{-28\left(-7\right)}}{2\times 7}$$

Multiply -28 times -7.

$$x=\frac{0±\sqrt{196}}{2\times 7}$$

Take the square root of 196.

$$x=\frac{0±14}{2\times 7}$$

Multiply 2 times 7.

$$x=\frac{0±14}{14}$$

Now solve the equation x=\frac{0±14}{14} when ± is plus. Divide 14 by 14.

$$x=1$$

Now solve the equation x=\frac{0±14}{14} when ± is minus. Divide -14 by 14.

$$x=-1$$

The equation is now solved.

$$x=1 x=-1$$