0=x^2+18x+8

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Solution for 0=x^2+18x+8 equation:


Simplifying
0 = x2 + 18x + 8

Reorder the terms:
0 = 8 + 18x + x2

Solving
0 = 8 + 18x + x2

Solving for variable 'x'.

Combine like terms: 0 + -8 = -8
-8 + -18x + -1x2 = 8 + 18x + x2 + -8 + -18x + -1x2

Reorder the terms:
-8 + -18x + -1x2 = 8 + -8 + 18x + -18x + x2 + -1x2

Combine like terms: 8 + -8 = 0
-8 + -18x + -1x2 = 0 + 18x + -18x + x2 + -1x2
-8 + -18x + -1x2 = 18x + -18x + x2 + -1x2

Combine like terms: 18x + -18x = 0
-8 + -18x + -1x2 = 0 + x2 + -1x2
-8 + -18x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-8 + -18x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8 + 18x + x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(8 + 18x + x2)' equal to zero and attempt to solve: Simplifying 8 + 18x + x2 = 0 Solving 8 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 18x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + 18x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 18x + x2 = 0 + -8 18x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 18x + x2 = -8 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = -8 + 81 Reorder the terms: 81 + 18x + x2 = -8 + 81 Combine like terms: -8 + 81 = 73 81 + 18x + x2 = 73 Factor a perfect square on the left side: (x + 9)(x + 9) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (x + 9) equal to 8.544003745 and -8.544003745.

Subproblem 1

x + 9 = 8.544003745 Simplifying x + 9 = 8.544003745 Reorder the terms: 9 + x = 8.544003745 Solving 9 + x = 8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 8.544003745 + -9 Combine like terms: 9 + -9 = 0 0 + x = 8.544003745 + -9 x = 8.544003745 + -9 Combine like terms: 8.544003745 + -9 = -0.455996255 x = -0.455996255 Simplifying x = -0.455996255

Subproblem 2

x + 9 = -8.544003745 Simplifying x + 9 = -8.544003745 Reorder the terms: 9 + x = -8.544003745 Solving 9 + x = -8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -8.544003745 + -9 Combine like terms: 9 + -9 = 0 0 + x = -8.544003745 + -9 x = -8.544003745 + -9 Combine like terms: -8.544003745 + -9 = -17.544003745 x = -17.544003745 Simplifying x = -17.544003745

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.455996255, -17.544003745}

Solution

x = {-0.455996255, -17.544003745}

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