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Simplifying 2x2 + 36x + 66 = 0 Reorder the terms: 66 + 36x + 2x2 = 0 Solving 66 + 36x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(33 + 18x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(33 + 18x + x2)' equal to zero and attempt to solve: Simplifying 33 + 18x + x2 = 0 Solving 33 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-33' to each side of the equation. 33 + 18x + -33 + x2 = 0 + -33 Reorder the terms: 33 + -33 + 18x + x2 = 0 + -33 Combine like terms: 33 + -33 = 0 0 + 18x + x2 = 0 + -33 18x + x2 = 0 + -33 Combine like terms: 0 + -33 = -33 18x + x2 = -33 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 = -33 + 81 Reorder the terms: 81 + 18x + x2 = -33 + 81 Combine like terms: -33 + 81 = 48 81 + 18x + x2 = 48 Factor a perfect square on the left side: (x + 9)(x + 9) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (x + 9) equal to 6.92820323 and -6.92820323.Subproblem 1
x + 9 = 6.92820323 Simplifying x + 9 = 6.92820323 Reorder the terms: 9 + x = 6.92820323 Solving 9 + x = 6.92820323 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 = 6.92820323 + -9 Combine like terms: 9 + -9 = 0 0 + x = 6.92820323 + -9 x = 6.92820323 + -9 Combine like terms: 6.92820323 + -9 = -2.07179677 x = -2.07179677 Simplifying x = -2.07179677Subproblem 2
x + 9 = -6.92820323 Simplifying x + 9 = -6.92820323 Reorder the terms: 9 + x = -6.92820323 Solving 9 + x = -6.92820323 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 = -6.92820323 + -9 Combine like terms: 9 + -9 = 0 0 + x = -6.92820323 + -9 x = -6.92820323 + -9 Combine like terms: -6.92820323 + -9 = -15.92820323 x = -15.92820323 Simplifying x = -15.92820323Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.07179677, -15.92820323}Solution
x = {-2.07179677, -15.92820323}
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