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Simplifying 2x + -30 + (x * x) = 180 Multiply x * x 2x + -30 + (x2) = 180 2x + -30 + x2 = 180 Reorder the terms: -30 + 2x + x2 = 180 Solving -30 + 2x + x2 = 180 Solving for variable 'x'. Reorder the terms: -30 + -180 + 2x + x2 = 180 + -180 Combine like terms: -30 + -180 = -210 -210 + 2x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -210 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '210' to each side of the equation. -210 + 2x + 210 + x2 = 0 + 210 Reorder the terms: -210 + 210 + 2x + x2 = 0 + 210 Combine like terms: -210 + 210 = 0 0 + 2x + x2 = 0 + 210 2x + x2 = 0 + 210 Combine like terms: 0 + 210 = 210 2x + x2 = 210 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 = 210 + 1 Reorder the terms: 1 + 2x + x2 = 210 + 1 Combine like terms: 210 + 1 = 211 1 + 2x + x2 = 211 Factor a perfect square on the left side: (x + 1)(x + 1) = 211 Calculate the square root of the right side: 14.525839046 Break this problem into two subproblems by setting (x + 1) equal to 14.525839046 and -14.525839046.Subproblem 1
x + 1 = 14.525839046 Simplifying x + 1 = 14.525839046 Reorder the terms: 1 + x = 14.525839046 Solving 1 + x = 14.525839046 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 = 14.525839046 + -1 Combine like terms: 1 + -1 = 0 0 + x = 14.525839046 + -1 x = 14.525839046 + -1 Combine like terms: 14.525839046 + -1 = 13.525839046 x = 13.525839046 Simplifying x = 13.525839046Subproblem 2
x + 1 = -14.525839046 Simplifying x + 1 = -14.525839046 Reorder the terms: 1 + x = -14.525839046 Solving 1 + x = -14.525839046 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 = -14.525839046 + -1 Combine like terms: 1 + -1 = 0 0 + x = -14.525839046 + -1 x = -14.525839046 + -1 Combine like terms: -14.525839046 + -1 = -15.525839046 x = -15.525839046 Simplifying x = -15.525839046Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.525839046, -15.525839046}
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