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Simplifying x2 + -12x = 139 Reorder the terms: -12x + x2 = 139 Solving -12x + x2 = 139 Solving for variable 'x'. Reorder the terms: -139 + -12x + x2 = 139 + -139 Combine like terms: 139 + -139 = 0 -139 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '139' to each side of the equation. -139 + -12x + 139 + x2 = 0 + 139 Reorder the terms: -139 + 139 + -12x + x2 = 0 + 139 Combine like terms: -139 + 139 = 0 0 + -12x + x2 = 0 + 139 -12x + x2 = 0 + 139 Combine like terms: 0 + 139 = 139 -12x + x2 = 139 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 139 + 36 Reorder the terms: 36 + -12x + x2 = 139 + 36 Combine like terms: 139 + 36 = 175 36 + -12x + x2 = 175 Factor a perfect square on the left side: (x + -6)(x + -6) = 175 Calculate the square root of the right side: 13.228756555 Break this problem into two subproblems by setting (x + -6) equal to 13.228756555 and -13.228756555.Subproblem 1
x + -6 = 13.228756555 Simplifying x + -6 = 13.228756555 Reorder the terms: -6 + x = 13.228756555 Solving -6 + x = 13.228756555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 13.228756555 + 6 Combine like terms: -6 + 6 = 0 0 + x = 13.228756555 + 6 x = 13.228756555 + 6 Combine like terms: 13.228756555 + 6 = 19.228756555 x = 19.228756555 Simplifying x = 19.228756555Subproblem 2
x + -6 = -13.228756555 Simplifying x + -6 = -13.228756555 Reorder the terms: -6 + x = -13.228756555 Solving -6 + x = -13.228756555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -13.228756555 + 6 Combine like terms: -6 + 6 = 0 0 + x = -13.228756555 + 6 x = -13.228756555 + 6 Combine like terms: -13.228756555 + 6 = -7.228756555 x = -7.228756555 Simplifying x = -7.228756555Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.228756555, -7.228756555}
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