Solve x^2+8x+8,3=6^2+8*6+8,3=

$$x ^ { 2 } + 8 x + 8,3 = 6 ^ { 2 } + 8 \cdot 6 + 8,3 =$$

Solve for x

$$x=-14$$

$$x=6$$

Steps Using Factoring

Calculate 6 to the power of 2 and get 36.

$$x^{2}+8x+8,3=36+8\times 6+8,3$$

Multiply 8 and 6 to get 48.

$$x^{2}+8x+8,3=36+48+8,3$$

Add 36 and 48 to get 84.

$$x^{2}+8x+8,3=84+8,3$$

Add 84 and 8,3 to get 92,3.

$$x^{2}+8x+8,3=92,3$$

Subtract 92,3 from both sides.

$$x^{2}+8x+8,3-92,3=0$$

Subtract 92,3 from 8,3 to get -84.

$$x^{2}+8x-84=0$$

To solve the equation, factor x^{2}+8x-84 using formula x^{2}+\left(a+b\right)x+ab=\left(x+a\right)\left(x+b\right). To find a and b, set up a system to be solved.

$$a+b=8 ab=-84$$

Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product -84.

$$-1;84 -2;42 -3;28 -4;21 -6;14 -7;12$$

Calculate the sum for each pair.

$$-1+84=83 -2+42=40 -3+28=25 -4+21=17 -6+14=8 -7+12=5$$

The solution is the pair that gives sum 8.

$$a=-6 b=14$$

Rewrite factored expression \left(x+a\right)\left(x+b\right) using the obtained values.

$$\left(x-6\right)\left(x+14\right)$$

To find equation solutions, solve x-6=0 and x+14=0.

$$x=6 x=-14$$

Steps Using Factoring By Grouping

Calculate 6 to the power of 2 and get 36.

$$x^{2}+8x+8,3=36+8\times 6+8,3$$

Multiply 8 and 6 to get 48.

$$x^{2}+8x+8,3=36+48+8,3$$

Add 36 and 48 to get 84.

$$x^{2}+8x+8,3=84+8,3$$

Add 84 and 8,3 to get 92,3.

$$x^{2}+8x+8,3=92,3$$

Subtract 92,3 from both sides.

$$x^{2}+8x+8,3-92,3=0$$

Subtract 92,3 from 8,3 to get -84.

$$x^{2}+8x-84=0$$

To solve the equation, factor the left hand side by grouping. First, left hand side needs to be rewritten as x^{2}+ax+bx-84. To find a and b, set up a system to be solved.

$$a+b=8 ab=1\left(-84\right)=-84$$

Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product -84.

$$-1;84 -2;42 -3;28 -4;21 -6;14 -7;12$$

Calculate the sum for each pair.

$$-1+84=83 -2+42=40 -3+28=25 -4+21=17 -6+14=8 -7+12=5$$

The solution is the pair that gives sum 8.

$$a=-6 b=14$$

Rewrite x^{2}+8x-84 as \left(x^{2}-6x\right)+\left(14x-84\right).

$$\left(x^{2}-6x\right)+\left(14x-84\right)$$

Factor out x in the first and 14 in the second group.

$$x\left(x-6\right)+14\left(x-6\right)$$

Factor out common term x-6 by using distributive property.

$$\left(x-6\right)\left(x+14\right)$$

To find equation solutions, solve x-6=0 and x+14=0.

$$x=6 x=-14$$

Steps Using the Quadratic Formula

Calculate 6 to the power of 2 and get 36.

$$x^{2}+8x+8,3=36+8\times 6+8,3$$

Multiply 8 and 6 to get 48.

$$x^{2}+8x+8,3=36+48+8,3$$

Add 36 and 48 to get 84.

$$x^{2}+8x+8,3=84+8,3$$

Add 84 and 8,3 to get 92,3.

$$x^{2}+8x+8,3=92,3$$

Subtract 92,3 from both sides.

$$x^{2}+8x+8,3-92,3=0$$

Subtract 92,3 from 8,3 to get -84.

$$x^{2}+8x-84=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 8 for b, and -84 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-84\right)}}{2}$$

Square 8.

$$x=\frac{-8±\sqrt{64-4\left(-84\right)}}{2}$$

Multiply -4 times -84.

$$x=\frac{-8±\sqrt{64+336}}{2}$$

Add 64 to 336.

$$x=\frac{-8±\sqrt{400}}{2}$$

Take the square root of 400.

$$x=\frac{-8±20}{2}$$

Now solve the equation x=\frac{-8±20}{2} when ± is plus. Add -8 to 20.

$$x=\frac{12}{2}$$

Divide 12 by 2.

$$x=6$$

Now solve the equation x=\frac{-8±20}{2} when ± is minus. Subtract 20 from -8.

$$x=-\frac{28}{2}$$

Divide -28 by 2.

$$x=-14$$

The equation is now solved.

$$x=6 x=-14$$

Steps for Completing the Square

Calculate 6 to the power of 2 and get 36.

$$x^{2}+8x+8,3=36+8\times 6+8,3$$

Multiply 8 and 6 to get 48.

$$x^{2}+8x+8,3=36+48+8,3$$

Add 36 and 48 to get 84.

$$x^{2}+8x+8,3=84+8,3$$

Add 84 and 8,3 to get 92,3.

$$x^{2}+8x+8,3=92,3$$

Subtract 8,3 from both sides.

$$x^{2}+8x=92,3-8,3$$

Subtract 8,3 from 92,3 to get 84.

$$x^{2}+8x=84$$

Divide 8, the coefficient of the x term, by 2 to get 4. Then add the square of 4 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+8x+4^{2}=84+4^{2}$$

Square 4.

$$x^{2}+8x+16=84+16$$

Add 84 to 16.

$$x^{2}+8x+16=100$$

Factor x^{2}+8x+16. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+4\right)^{2}=100$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+4\right)^{2}}=\sqrt{100}$$

Simplify.

$$x+4=10 x+4=-10$$

Subtract 4 from both sides of the equation.

$$x=6 x=-14$$