x^2+8x-18=3

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Solution for x^2+8x-18=3 equation:


Simplifying
x2 + 8x + -18 = 3

Reorder the terms:
-18 + 8x + x2 = 3

Solving
-18 + 8x + x2 = 3

Solving for variable 'x'.

Reorder the terms:
-18 + -3 + 8x + x2 = 3 + -3

Combine like terms: -18 + -3 = -21
-21 + 8x + x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-21 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 8x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + 8x + x2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 8x + x2 = 0 + 21
8x + x2 = 0 + 21

Combine like terms: 0 + 21 = 21
8x + x2 = 21

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 21 + 16

Reorder the terms:
16 + 8x + x2 = 21 + 16

Combine like terms: 21 + 16 = 37
16 + 8x + x2 = 37

Factor a perfect square on the left side:
(x + 4)(x + 4) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(x + 4) equal to 6.08276253 and -6.08276253.

Subproblem 1

x + 4 = 6.08276253 Simplifying x + 4 = 6.08276253 Reorder the terms: 4 + x = 6.08276253 Solving 4 + x = 6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 6.08276253 + -4 Combine like terms: 4 + -4 = 0 0 + x = 6.08276253 + -4 x = 6.08276253 + -4 Combine like terms: 6.08276253 + -4 = 2.08276253 x = 2.08276253 Simplifying x = 2.08276253

Subproblem 2

x + 4 = -6.08276253 Simplifying x + 4 = -6.08276253 Reorder the terms: 4 + x = -6.08276253 Solving 4 + x = -6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -6.08276253 + -4 Combine like terms: 4 + -4 = 0 0 + x = -6.08276253 + -4 x = -6.08276253 + -4 Combine like terms: -6.08276253 + -4 = -10.08276253 x = -10.08276253 Simplifying x = -10.08276253

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.08276253, -10.08276253}

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