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Simplifying 4x + 11 + x2 + -10 = 180 Reorder the terms: 11 + -10 + 4x + x2 = 180 Combine like terms: 11 + -10 = 1 1 + 4x + x2 = 180 Solving 1 + 4x + x2 = 180 Solving for variable 'x'. Reorder the terms: 1 + -180 + 4x + x2 = 180 + -180 Combine like terms: 1 + -180 = -179 -179 + 4x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -179 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '179' to each side of the equation. -179 + 4x + 179 + x2 = 0 + 179 Reorder the terms: -179 + 179 + 4x + x2 = 0 + 179 Combine like terms: -179 + 179 = 0 0 + 4x + x2 = 0 + 179 4x + x2 = 0 + 179 Combine like terms: 0 + 179 = 179 4x + x2 = 179 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 = 179 + 4 Reorder the terms: 4 + 4x + x2 = 179 + 4 Combine like terms: 179 + 4 = 183 4 + 4x + x2 = 183 Factor a perfect square on the left side: (x + 2)(x + 2) = 183 Calculate the square root of the right side: 13.527749258 Break this problem into two subproblems by setting (x + 2) equal to 13.527749258 and -13.527749258.Subproblem 1
x + 2 = 13.527749258 Simplifying x + 2 = 13.527749258 Reorder the terms: 2 + x = 13.527749258 Solving 2 + x = 13.527749258 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 = 13.527749258 + -2 Combine like terms: 2 + -2 = 0 0 + x = 13.527749258 + -2 x = 13.527749258 + -2 Combine like terms: 13.527749258 + -2 = 11.527749258 x = 11.527749258 Simplifying x = 11.527749258Subproblem 2
x + 2 = -13.527749258 Simplifying x + 2 = -13.527749258 Reorder the terms: 2 + x = -13.527749258 Solving 2 + x = -13.527749258 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 = -13.527749258 + -2 Combine like terms: 2 + -2 = 0 0 + x = -13.527749258 + -2 x = -13.527749258 + -2 Combine like terms: -13.527749258 + -2 = -15.527749258 x = -15.527749258 Simplifying x = -15.527749258Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.527749258, -15.527749258}
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