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Simplifying x2 + 33x + 36 = 0 Reorder the terms: 36 + 33x + x2 = 0 Solving 36 + 33x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + 33x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + 33x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + 33x + x2 = 0 + -36 33x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 33x + x2 = -36 The x term is 33x. Take half its coefficient (16.5). Square it (272.25) and add it to both sides. Add '272.25' to each side of the equation. 33x + 272.25 + x2 = -36 + 272.25 Reorder the terms: 272.25 + 33x + x2 = -36 + 272.25 Combine like terms: -36 + 272.25 = 236.25 272.25 + 33x + x2 = 236.25 Factor a perfect square on the left side: (x + 16.5)(x + 16.5) = 236.25 Calculate the square root of the right side: 15.370426149 Break this problem into two subproblems by setting (x + 16.5) equal to 15.370426149 and -15.370426149.Subproblem 1
x + 16.5 = 15.370426149 Simplifying x + 16.5 = 15.370426149 Reorder the terms: 16.5 + x = 15.370426149 Solving 16.5 + x = 15.370426149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.5' to each side of the equation. 16.5 + -16.5 + x = 15.370426149 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + x = 15.370426149 + -16.5 x = 15.370426149 + -16.5 Combine like terms: 15.370426149 + -16.5 = -1.129573851 x = -1.129573851 Simplifying x = -1.129573851Subproblem 2
x + 16.5 = -15.370426149 Simplifying x + 16.5 = -15.370426149 Reorder the terms: 16.5 + x = -15.370426149 Solving 16.5 + x = -15.370426149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.5' to each side of the equation. 16.5 + -16.5 + x = -15.370426149 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + x = -15.370426149 + -16.5 x = -15.370426149 + -16.5 Combine like terms: -15.370426149 + -16.5 = -31.870426149 x = -31.870426149 Simplifying x = -31.870426149Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.129573851, -31.870426149}
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