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Simplifying x2 + -15x + 2 = 0 Reorder the terms: 2 + -15x + x2 = 0 Solving 2 + -15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -15x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -15x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -15x + x2 = 0 + -2 -15x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -15x + x2 = -2 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -2 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -2 + 56.25 Combine like terms: -2 + 56.25 = 54.25 56.25 + -15x + x2 = 54.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 54.25 Calculate the square root of the right side: 7.365459931 Break this problem into two subproblems by setting (x + -7.5) equal to 7.365459931 and -7.365459931.Subproblem 1
x + -7.5 = 7.365459931 Simplifying x + -7.5 = 7.365459931 Reorder the terms: -7.5 + x = 7.365459931 Solving -7.5 + x = 7.365459931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 7.365459931 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 7.365459931 + 7.5 x = 7.365459931 + 7.5 Combine like terms: 7.365459931 + 7.5 = 14.865459931 x = 14.865459931 Simplifying x = 14.865459931Subproblem 2
x + -7.5 = -7.365459931 Simplifying x + -7.5 = -7.365459931 Reorder the terms: -7.5 + x = -7.365459931 Solving -7.5 + x = -7.365459931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -7.365459931 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -7.365459931 + 7.5 x = -7.365459931 + 7.5 Combine like terms: -7.365459931 + 7.5 = 0.134540069 x = 0.134540069 Simplifying x = 0.134540069Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.865459931, 0.134540069}
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