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Simplifying x2 + 6x + -20 = 180 Reorder the terms: -20 + 6x + x2 = 180 Solving -20 + 6x + x2 = 180 Solving for variable 'x'. Reorder the terms: -20 + -180 + 6x + x2 = 180 + -180 Combine like terms: -20 + -180 = -200 -200 + 6x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -200 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '200' to each side of the equation. -200 + 6x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + 6x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 6x + x2 = 0 + 200 6x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 6x + x2 = 200 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 200 + 9 Reorder the terms: 9 + 6x + x2 = 200 + 9 Combine like terms: 200 + 9 = 209 9 + 6x + x2 = 209 Factor a perfect square on the left side: (x + 3)(x + 3) = 209 Calculate the square root of the right side: 14.456832295 Break this problem into two subproblems by setting (x + 3) equal to 14.456832295 and -14.456832295.Subproblem 1
x + 3 = 14.456832295 Simplifying x + 3 = 14.456832295 Reorder the terms: 3 + x = 14.456832295 Solving 3 + x = 14.456832295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 14.456832295 + -3 Combine like terms: 3 + -3 = 0 0 + x = 14.456832295 + -3 x = 14.456832295 + -3 Combine like terms: 14.456832295 + -3 = 11.456832295 x = 11.456832295 Simplifying x = 11.456832295Subproblem 2
x + 3 = -14.456832295 Simplifying x + 3 = -14.456832295 Reorder the terms: 3 + x = -14.456832295 Solving 3 + x = -14.456832295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -14.456832295 + -3 Combine like terms: 3 + -3 = 0 0 + x = -14.456832295 + -3 x = -14.456832295 + -3 Combine like terms: -14.456832295 + -3 = -17.456832295 x = -17.456832295 Simplifying x = -17.456832295Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.456832295, -17.456832295}
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