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Simplifying x2 + -6x + 48 = 180 Reorder the terms: 48 + -6x + x2 = 180 Solving 48 + -6x + x2 = 180 Solving for variable 'x'. Reorder the terms: 48 + -180 + -6x + x2 = 180 + -180 Combine like terms: 48 + -180 = -132 -132 + -6x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -132 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '132' to each side of the equation. -132 + -6x + 132 + x2 = 0 + 132 Reorder the terms: -132 + 132 + -6x + x2 = 0 + 132 Combine like terms: -132 + 132 = 0 0 + -6x + x2 = 0 + 132 -6x + x2 = 0 + 132 Combine like terms: 0 + 132 = 132 -6x + x2 = 132 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 = 132 + 9 Reorder the terms: 9 + -6x + x2 = 132 + 9 Combine like terms: 132 + 9 = 141 9 + -6x + x2 = 141 Factor a perfect square on the left side: (x + -3)(x + -3) = 141 Calculate the square root of the right side: 11.874342087 Break this problem into two subproblems by setting (x + -3) equal to 11.874342087 and -11.874342087.Subproblem 1
x + -3 = 11.874342087 Simplifying x + -3 = 11.874342087 Reorder the terms: -3 + x = 11.874342087 Solving -3 + x = 11.874342087 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 = 11.874342087 + 3 Combine like terms: -3 + 3 = 0 0 + x = 11.874342087 + 3 x = 11.874342087 + 3 Combine like terms: 11.874342087 + 3 = 14.874342087 x = 14.874342087 Simplifying x = 14.874342087Subproblem 2
x + -3 = -11.874342087 Simplifying x + -3 = -11.874342087 Reorder the terms: -3 + x = -11.874342087 Solving -3 + x = -11.874342087 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 = -11.874342087 + 3 Combine like terms: -3 + 3 = 0 0 + x = -11.874342087 + 3 x = -11.874342087 + 3 Combine like terms: -11.874342087 + 3 = -8.874342087 x = -8.874342087 Simplifying x = -8.874342087Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.874342087, -8.874342087}
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