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Simplifying 2x2 + 18x = 228 Reorder the terms: 18x + 2x2 = 228 Solving 18x + 2x2 = 228 Solving for variable 'x'. Reorder the terms: -228 + 18x + 2x2 = 228 + -228 Combine like terms: 228 + -228 = 0 -228 + 18x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-114 + 9x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-114 + 9x + x2)' equal to zero and attempt to solve: Simplifying -114 + 9x + x2 = 0 Solving -114 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '114' to each side of the equation. -114 + 9x + 114 + x2 = 0 + 114 Reorder the terms: -114 + 114 + 9x + x2 = 0 + 114 Combine like terms: -114 + 114 = 0 0 + 9x + x2 = 0 + 114 9x + x2 = 0 + 114 Combine like terms: 0 + 114 = 114 9x + x2 = 114 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 = 114 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 114 + 20.25 Combine like terms: 114 + 20.25 = 134.25 20.25 + 9x + x2 = 134.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 134.25 Calculate the square root of the right side: 11.586630226 Break this problem into two subproblems by setting (x + 4.5) equal to 11.586630226 and -11.586630226.Subproblem 1
x + 4.5 = 11.586630226 Simplifying x + 4.5 = 11.586630226 Reorder the terms: 4.5 + x = 11.586630226 Solving 4.5 + x = 11.586630226 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 = 11.586630226 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 11.586630226 + -4.5 x = 11.586630226 + -4.5 Combine like terms: 11.586630226 + -4.5 = 7.086630226 x = 7.086630226 Simplifying x = 7.086630226Subproblem 2
x + 4.5 = -11.586630226 Simplifying x + 4.5 = -11.586630226 Reorder the terms: 4.5 + x = -11.586630226 Solving 4.5 + x = -11.586630226 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 = -11.586630226 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -11.586630226 + -4.5 x = -11.586630226 + -4.5 Combine like terms: -11.586630226 + -4.5 = -16.086630226 x = -16.086630226 Simplifying x = -16.086630226Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.086630226, -16.086630226}Solution
x = {7.086630226, -16.086630226}
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