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Simplifying x2 + -6x = 180 Reorder the terms: -6x + x2 = 180 Solving -6x + x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -6x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + -6x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + -6x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + -6x + x2 = 0 + 180 -6x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 -6x + x2 = 180 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 = 180 + 9 Reorder the terms: 9 + -6x + x2 = 180 + 9 Combine like terms: 180 + 9 = 189 9 + -6x + x2 = 189 Factor a perfect square on the left side: (x + -3)(x + -3) = 189 Calculate the square root of the right side: 13.747727085 Break this problem into two subproblems by setting (x + -3) equal to 13.747727085 and -13.747727085.Subproblem 1
x + -3 = 13.747727085 Simplifying x + -3 = 13.747727085 Reorder the terms: -3 + x = 13.747727085 Solving -3 + x = 13.747727085 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 = 13.747727085 + 3 Combine like terms: -3 + 3 = 0 0 + x = 13.747727085 + 3 x = 13.747727085 + 3 Combine like terms: 13.747727085 + 3 = 16.747727085 x = 16.747727085 Simplifying x = 16.747727085Subproblem 2
x + -3 = -13.747727085 Simplifying x + -3 = -13.747727085 Reorder the terms: -3 + x = -13.747727085 Solving -3 + x = -13.747727085 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 = -13.747727085 + 3 Combine like terms: -3 + 3 = 0 0 + x = -13.747727085 + 3 x = -13.747727085 + 3 Combine like terms: -13.747727085 + 3 = -10.747727085 x = -10.747727085 Simplifying x = -10.747727085Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.747727085, -10.747727085}
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