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Simplifying x(x + 2) = 132 Reorder the terms: x(2 + x) = 132 (2 * x + x * x) = 132 (2x + x2) = 132 Solving 2x + x2 = 132 Solving for variable 'x'. Reorder the terms: -132 + 2x + x2 = 132 + -132 Combine like terms: 132 + -132 = 0 -132 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '132' to each side of the equation. -132 + 2x + 132 + x2 = 0 + 132 Reorder the terms: -132 + 132 + 2x + x2 = 0 + 132 Combine like terms: -132 + 132 = 0 0 + 2x + x2 = 0 + 132 2x + x2 = 0 + 132 Combine like terms: 0 + 132 = 132 2x + x2 = 132 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 132 + 1 Reorder the terms: 1 + 2x + x2 = 132 + 1 Combine like terms: 132 + 1 = 133 1 + 2x + x2 = 133 Factor a perfect square on the left side: (x + 1)(x + 1) = 133 Calculate the square root of the right side: 11.532562595 Break this problem into two subproblems by setting (x + 1) equal to 11.532562595 and -11.532562595.Subproblem 1
x + 1 = 11.532562595 Simplifying x + 1 = 11.532562595 Reorder the terms: 1 + x = 11.532562595 Solving 1 + x = 11.532562595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 11.532562595 + -1 Combine like terms: 1 + -1 = 0 0 + x = 11.532562595 + -1 x = 11.532562595 + -1 Combine like terms: 11.532562595 + -1 = 10.532562595 x = 10.532562595 Simplifying x = 10.532562595Subproblem 2
x + 1 = -11.532562595 Simplifying x + 1 = -11.532562595 Reorder the terms: 1 + x = -11.532562595 Solving 1 + x = -11.532562595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -11.532562595 + -1 Combine like terms: 1 + -1 = 0 0 + x = -11.532562595 + -1 x = -11.532562595 + -1 Combine like terms: -11.532562595 + -1 = -12.532562595 x = -12.532562595 Simplifying x = -12.532562595Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.532562595, -12.532562595}
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