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Simplifying 2x2 + 18x + -18 = 0 Reorder the terms: -18 + 18x + 2x2 = 0 Solving -18 + 18x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 9x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + 9x + x2)' equal to zero and attempt to solve: Simplifying -9 + 9x + x2 = 0 Solving -9 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 9x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 9x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 9x + x2 = 0 + 9 9x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 9x + x2 = 9 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 9 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 9 + 20.25 Combine like terms: 9 + 20.25 = 29.25 20.25 + 9x + x2 = 29.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (x + 4.5) equal to 5.408326913 and -5.408326913.Subproblem 1
x + 4.5 = 5.408326913 Simplifying x + 4.5 = 5.408326913 Reorder the terms: 4.5 + x = 5.408326913 Solving 4.5 + x = 5.408326913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 5.408326913 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 5.408326913 + -4.5 x = 5.408326913 + -4.5 Combine like terms: 5.408326913 + -4.5 = 0.908326913 x = 0.908326913 Simplifying x = 0.908326913Subproblem 2
x + 4.5 = -5.408326913 Simplifying x + 4.5 = -5.408326913 Reorder the terms: 4.5 + x = -5.408326913 Solving 4.5 + x = -5.408326913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -5.408326913 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -5.408326913 + -4.5 x = -5.408326913 + -4.5 Combine like terms: -5.408326913 + -4.5 = -9.908326913 x = -9.908326913 Simplifying x = -9.908326913Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.908326913, -9.908326913}Solution
x = {0.908326913, -9.908326913}
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