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Simplifying 4x + -12 + x2 = 120 Reorder the terms: -12 + 4x + x2 = 120 Solving -12 + 4x + x2 = 120 Solving for variable 'x'. Reorder the terms: -12 + -120 + 4x + x2 = 120 + -120 Combine like terms: -12 + -120 = -132 -132 + 4x + x2 = 120 + -120 Combine like terms: 120 + -120 = 0 -132 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '132' to each side of the equation. -132 + 4x + 132 + x2 = 0 + 132 Reorder the terms: -132 + 132 + 4x + x2 = 0 + 132 Combine like terms: -132 + 132 = 0 0 + 4x + x2 = 0 + 132 4x + x2 = 0 + 132 Combine like terms: 0 + 132 = 132 4x + x2 = 132 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 132 + 4 Reorder the terms: 4 + 4x + x2 = 132 + 4 Combine like terms: 132 + 4 = 136 4 + 4x + x2 = 136 Factor a perfect square on the left side: (x + 2)(x + 2) = 136 Calculate the square root of the right side: 11.66190379 Break this problem into two subproblems by setting (x + 2) equal to 11.66190379 and -11.66190379.Subproblem 1
x + 2 = 11.66190379 Simplifying x + 2 = 11.66190379 Reorder the terms: 2 + x = 11.66190379 Solving 2 + x = 11.66190379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 11.66190379 + -2 Combine like terms: 2 + -2 = 0 0 + x = 11.66190379 + -2 x = 11.66190379 + -2 Combine like terms: 11.66190379 + -2 = 9.66190379 x = 9.66190379 Simplifying x = 9.66190379Subproblem 2
x + 2 = -11.66190379 Simplifying x + 2 = -11.66190379 Reorder the terms: 2 + x = -11.66190379 Solving 2 + x = -11.66190379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -11.66190379 + -2 Combine like terms: 2 + -2 = 0 0 + x = -11.66190379 + -2 x = -11.66190379 + -2 Combine like terms: -11.66190379 + -2 = -13.66190379 x = -13.66190379 Simplifying x = -13.66190379Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.66190379, -13.66190379}
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