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Simplifying 2x2 + 36x + -252 = 0 Reorder the terms: -252 + 36x + 2x2 = 0 Solving -252 + 36x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-126 + 18x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-126 + 18x + x2)' equal to zero and attempt to solve: Simplifying -126 + 18x + x2 = 0 Solving -126 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '126' to each side of the equation. -126 + 18x + 126 + x2 = 0 + 126 Reorder the terms: -126 + 126 + 18x + x2 = 0 + 126 Combine like terms: -126 + 126 = 0 0 + 18x + x2 = 0 + 126 18x + x2 = 0 + 126 Combine like terms: 0 + 126 = 126 18x + x2 = 126 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 = 126 + 81 Reorder the terms: 81 + 18x + x2 = 126 + 81 Combine like terms: 126 + 81 = 207 81 + 18x + x2 = 207 Factor a perfect square on the left side: (x + 9)(x + 9) = 207 Calculate the square root of the right side: 14.38749457 Break this problem into two subproblems by setting (x + 9) equal to 14.38749457 and -14.38749457.Subproblem 1
x + 9 = 14.38749457 Simplifying x + 9 = 14.38749457 Reorder the terms: 9 + x = 14.38749457 Solving 9 + x = 14.38749457 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 = 14.38749457 + -9 Combine like terms: 9 + -9 = 0 0 + x = 14.38749457 + -9 x = 14.38749457 + -9 Combine like terms: 14.38749457 + -9 = 5.38749457 x = 5.38749457 Simplifying x = 5.38749457Subproblem 2
x + 9 = -14.38749457 Simplifying x + 9 = -14.38749457 Reorder the terms: 9 + x = -14.38749457 Solving 9 + x = -14.38749457 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 = -14.38749457 + -9 Combine like terms: 9 + -9 = 0 0 + x = -14.38749457 + -9 x = -14.38749457 + -9 Combine like terms: -14.38749457 + -9 = -23.38749457 x = -23.38749457 Simplifying x = -23.38749457Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.38749457, -23.38749457}Solution
x = {5.38749457, -23.38749457}
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