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Simplifying x2 + 3x + 11x + 20 = 180 Reorder the terms: 20 + 3x + 11x + x2 = 180 Combine like terms: 3x + 11x = 14x 20 + 14x + x2 = 180 Solving 20 + 14x + x2 = 180 Solving for variable 'x'. Reorder the terms: 20 + -180 + 14x + x2 = 180 + -180 Combine like terms: 20 + -180 = -160 -160 + 14x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -160 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '160' to each side of the equation. -160 + 14x + 160 + x2 = 0 + 160 Reorder the terms: -160 + 160 + 14x + x2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + 14x + x2 = 0 + 160 14x + x2 = 0 + 160 Combine like terms: 0 + 160 = 160 14x + x2 = 160 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 160 + 49 Reorder the terms: 49 + 14x + x2 = 160 + 49 Combine like terms: 160 + 49 = 209 49 + 14x + x2 = 209 Factor a perfect square on the left side: (x + 7)(x + 7) = 209 Calculate the square root of the right side: 14.456832295 Break this problem into two subproblems by setting (x + 7) equal to 14.456832295 and -14.456832295.Subproblem 1
x + 7 = 14.456832295 Simplifying x + 7 = 14.456832295 Reorder the terms: 7 + x = 14.456832295 Solving 7 + x = 14.456832295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 14.456832295 + -7 Combine like terms: 7 + -7 = 0 0 + x = 14.456832295 + -7 x = 14.456832295 + -7 Combine like terms: 14.456832295 + -7 = 7.456832295 x = 7.456832295 Simplifying x = 7.456832295Subproblem 2
x + 7 = -14.456832295 Simplifying x + 7 = -14.456832295 Reorder the terms: 7 + x = -14.456832295 Solving 7 + x = -14.456832295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -14.456832295 + -7 Combine like terms: 7 + -7 = 0 0 + x = -14.456832295 + -7 x = -14.456832295 + -7 Combine like terms: -14.456832295 + -7 = -21.456832295 x = -21.456832295 Simplifying x = -21.456832295Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.456832295, -21.456832295}
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