Solve x^2+4*(x+3)=10

$${ x }^{ 2 } +4 \times (x+3)=10$$

Solve for x

$$x=\sqrt{2}-2\approx -0.585786438$$

$$x=-\sqrt{2}-2\approx -3.414213562$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 4 by x+3.

$$x^{2}+4x+12=10$$

Subtract 10 from both sides.

$$x^{2}+4x+12-10=0$$

Subtract 10 from 12 to get 2.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 4 for b, and 2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 4.

$$x=\frac{-4±\sqrt{16-4\times 2}}{2}$$

Multiply -4 times 2.

$$x=\frac{-4±\sqrt{16-8}}{2}$$

Add 16 to -8.

$$x=\frac{-4±\sqrt{8}}{2}$$

Take the square root of 8.

$$x=\frac{-4±2\sqrt{2}}{2}$$

Now solve the equation x=\frac{-4±2\sqrt{2}}{2} when ± is plus. Add -4 to 2\sqrt{2}.

$$x=\frac{2\sqrt{2}-4}{2}$$

Divide -4+2\sqrt{2} by 2.

$$x=\sqrt{2}-2$$

Now solve the equation x=\frac{-4±2\sqrt{2}}{2} when ± is minus. Subtract 2\sqrt{2} from -4.

$$x=\frac{-2\sqrt{2}-4}{2}$$

Divide -4-2\sqrt{2} by 2.

$$x=-\sqrt{2}-2$$

The equation is now solved.

$$x=\sqrt{2}-2 x=-\sqrt{2}-2$$

Steps for Completing the Square

Use the distributive property to multiply 4 by x+3.

$$x^{2}+4x+12=10$$

Subtract 12 from both sides.

$$x^{2}+4x=10-12$$

Subtract 12 from 10 to get -2.

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

Divide 4, the coefficient of the x term, by 2 to get 2. Then add the square of 2 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

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

Square 2.

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

Add -2 to 4.

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

Factor x^{2}+4x+4. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+2\right)^{2}=2$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+2\right)^{2}}=\sqrt{2}$$

Simplify.

$$x+2=\sqrt{2} x+2=-\sqrt{2}$$

Subtract 2 from both sides of the equation.

$$x=\sqrt{2}-2 x=-\sqrt{2}-2$$