Solve x^2+8x-36*13=0

$$x ^ { 2 } + 8 x - 36 \cdot 13 = 0$$

Solve for x

$$x=-26$$

$$x=18$$

Steps Using Factoring

Multiply 36 and 13 to get 468.

$$x^{2}+8x-468=0$$

To solve the equation, factor x^{2}+8x-468 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.

$$a+b=8 ab=-468$$

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 -468.

$$-1,468 -2,234 -3,156 -4,117 -6,78 -9,52 -12,39 -13,36 -18,26$$

Calculate the sum for each pair.

$$-1+468=467 -2+234=232 -3+156=153 -4+117=113 -6+78=72 -9+52=43 -12+39=27 -13+36=23 -18+26=8$$

The solution is the pair that gives sum 8.

$$a=-18 b=26$$

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

$$\left(x-18\right)\left(x+26\right)$$

To find equation solutions, solve x-18=0 and x+26=0.

$$x=18 x=-26$$

Steps Using Factoring By Grouping

Multiply 36 and 13 to get 468.

$$x^{2}+8x-468=0$$

To solve the equation, factor the left hand side by grouping. First, left hand side needs to be rewritten as x^{2}+ax+bx-468. To find a and b, set up a system to be solved.

$$a+b=8 ab=1\left(-468\right)=-468$$

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 -468.

$$-1,468 -2,234 -3,156 -4,117 -6,78 -9,52 -12,39 -13,36 -18,26$$

Calculate the sum for each pair.

$$-1+468=467 -2+234=232 -3+156=153 -4+117=113 -6+78=72 -9+52=43 -12+39=27 -13+36=23 -18+26=8$$

The solution is the pair that gives sum 8.

$$a=-18 b=26$$

Rewrite x^{2}+8x-468 as \left(x^{2}-18x\right)+\left(26x-468\right).

$$\left(x^{2}-18x\right)+\left(26x-468\right)$$

Factor out x in the first and 26 in the second group.

$$x\left(x-18\right)+26\left(x-18\right)$$

Factor out common term x-18 by using distributive property.

$$\left(x-18\right)\left(x+26\right)$$

To find equation solutions, solve x-18=0 and x+26=0.

$$x=18 x=-26$$

Steps Using the Quadratic Formula

Multiply 36 and 13 to get 468.

$$x^{2}+8x-468=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 8 for b, and -468 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-468\right)}}{2}$$

Square 8.

$$x=\frac{-8±\sqrt{64-4\left(-468\right)}}{2}$$

Multiply -4 times -468.

$$x=\frac{-8±\sqrt{64+1872}}{2}$$

Add 64 to 1872.

$$x=\frac{-8±\sqrt{1936}}{2}$$

Take the square root of 1936.

$$x=\frac{-8±44}{2}$$

Now solve the equation x=\frac{-8±44}{2} when ± is plus. Add -8 to 44.

$$x=\frac{36}{2}$$

Divide 36 by 2.

$$x=18$$

Now solve the equation x=\frac{-8±44}{2} when ± is minus. Subtract 44 from -8.

$$x=-\frac{52}{2}$$

Divide -52 by 2.

$$x=-26$$

The equation is now solved.

$$x=18 x=-26$$

Steps for Completing the Square

Multiply 36 and 13 to get 468.

$$x^{2}+8x-468=0$$

Add 468 to both sides. Anything plus zero gives itself.

$$x^{2}+8x=468$$

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.

$$x^{2}+8x+4^{2}=468+4^{2}$$

Square 4.

$$x^{2}+8x+16=468+16$$

Add 468 to 16.

$$x^{2}+8x+16=484$$

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}.

$$\left(x+4\right)^{2}=484$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+4\right)^{2}}=\sqrt{484}$$

Simplify.

$$x+4=22 x+4=-22$$

Subtract 4 from both sides of the equation.

$$x=18 x=-26$$