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Simplifying 2x2 + 36x + -4 = 0 Reorder the terms: -4 + 36x + 2x2 = 0 Solving -4 + 36x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 18x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + 18x + x2)' equal to zero and attempt to solve: Simplifying -2 + 18x + x2 = 0 Solving -2 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 18x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 18x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 18x + x2 = 0 + 2 18x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 18x + x2 = 2 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 = 2 + 81 Reorder the terms: 81 + 18x + x2 = 2 + 81 Combine like terms: 2 + 81 = 83 81 + 18x + x2 = 83 Factor a perfect square on the left side: (x + 9)(x + 9) = 83 Calculate the square root of the right side: 9.110433579 Break this problem into two subproblems by setting (x + 9) equal to 9.110433579 and -9.110433579.Subproblem 1
x + 9 = 9.110433579 Simplifying x + 9 = 9.110433579 Reorder the terms: 9 + x = 9.110433579 Solving 9 + x = 9.110433579 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 = 9.110433579 + -9 Combine like terms: 9 + -9 = 0 0 + x = 9.110433579 + -9 x = 9.110433579 + -9 Combine like terms: 9.110433579 + -9 = 0.110433579 x = 0.110433579 Simplifying x = 0.110433579Subproblem 2
x + 9 = -9.110433579 Simplifying x + 9 = -9.110433579 Reorder the terms: 9 + x = -9.110433579 Solving 9 + x = -9.110433579 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 = -9.110433579 + -9 Combine like terms: 9 + -9 = 0 0 + x = -9.110433579 + -9 x = -9.110433579 + -9 Combine like terms: -9.110433579 + -9 = -18.110433579 x = -18.110433579 Simplifying x = -18.110433579Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.110433579, -18.110433579}Solution
x = {0.110433579, -18.110433579}
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