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Simplifying x2 + 19x + 36 = 0 Reorder the terms: 36 + 19x + x2 = 0 Solving 36 + 19x + 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 + 19x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + 19x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + 19x + x2 = 0 + -36 19x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 19x + x2 = -36 The x term is 19x. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19x + 90.25 + x2 = -36 + 90.25 Reorder the terms: 90.25 + 19x + x2 = -36 + 90.25 Combine like terms: -36 + 90.25 = 54.25 90.25 + 19x + x2 = 54.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 54.25 Calculate the square root of the right side: 7.365459931 Break this problem into two subproblems by setting (x + 9.5) equal to 7.365459931 and -7.365459931.Subproblem 1
x + 9.5 = 7.365459931 Simplifying x + 9.5 = 7.365459931 Reorder the terms: 9.5 + x = 7.365459931 Solving 9.5 + x = 7.365459931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 7.365459931 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 7.365459931 + -9.5 x = 7.365459931 + -9.5 Combine like terms: 7.365459931 + -9.5 = -2.134540069 x = -2.134540069 Simplifying x = -2.134540069Subproblem 2
x + 9.5 = -7.365459931 Simplifying x + 9.5 = -7.365459931 Reorder the terms: 9.5 + x = -7.365459931 Solving 9.5 + x = -7.365459931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -7.365459931 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -7.365459931 + -9.5 x = -7.365459931 + -9.5 Combine like terms: -7.365459931 + -9.5 = -16.865459931 x = -16.865459931 Simplifying x = -16.865459931Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.134540069, -16.865459931}
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