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Simplifying x2 + 3x + -52 = 0 Reorder the terms: -52 + 3x + x2 = 0 Solving -52 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + 3x + 52 + x2 = 0 + 52 Reorder the terms: -52 + 52 + 3x + x2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + 3x + x2 = 0 + 52 3x + x2 = 0 + 52 Combine like terms: 0 + 52 = 52 3x + x2 = 52 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 52 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 52 + 2.25 Combine like terms: 52 + 2.25 = 54.25 2.25 + 3x + x2 = 54.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 54.25 Calculate the square root of the right side: 7.365459931 Break this problem into two subproblems by setting (x + 1.5) equal to 7.365459931 and -7.365459931.Subproblem 1
x + 1.5 = 7.365459931 Simplifying x + 1.5 = 7.365459931 Reorder the terms: 1.5 + x = 7.365459931 Solving 1.5 + x = 7.365459931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 7.365459931 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 7.365459931 + -1.5 x = 7.365459931 + -1.5 Combine like terms: 7.365459931 + -1.5 = 5.865459931 x = 5.865459931 Simplifying x = 5.865459931Subproblem 2
x + 1.5 = -7.365459931 Simplifying x + 1.5 = -7.365459931 Reorder the terms: 1.5 + x = -7.365459931 Solving 1.5 + x = -7.365459931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -7.365459931 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -7.365459931 + -1.5 x = -7.365459931 + -1.5 Combine like terms: -7.365459931 + -1.5 = -8.865459931 x = -8.865459931 Simplifying x = -8.865459931Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.865459931, -8.865459931}
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