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Simplifying x(x + -27) + 127 = 0 Reorder the terms: x(-27 + x) + 127 = 0 (-27 * x + x * x) + 127 = 0 (-27x + x2) + 127 = 0 Reorder the terms: 127 + -27x + x2 = 0 Solving 127 + -27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-127' to each side of the equation. 127 + -27x + -127 + x2 = 0 + -127 Reorder the terms: 127 + -127 + -27x + x2 = 0 + -127 Combine like terms: 127 + -127 = 0 0 + -27x + x2 = 0 + -127 -27x + x2 = 0 + -127 Combine like terms: 0 + -127 = -127 -27x + x2 = -127 The x term is -27x. Take half its coefficient (-13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. -27x + 182.25 + x2 = -127 + 182.25 Reorder the terms: 182.25 + -27x + x2 = -127 + 182.25 Combine like terms: -127 + 182.25 = 55.25 182.25 + -27x + x2 = 55.25 Factor a perfect square on the left side: (x + -13.5)(x + -13.5) = 55.25 Calculate the square root of the right side: 7.433034374 Break this problem into two subproblems by setting (x + -13.5) equal to 7.433034374 and -7.433034374.Subproblem 1
x + -13.5 = 7.433034374 Simplifying x + -13.5 = 7.433034374 Reorder the terms: -13.5 + x = 7.433034374 Solving -13.5 + x = 7.433034374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = 7.433034374 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = 7.433034374 + 13.5 x = 7.433034374 + 13.5 Combine like terms: 7.433034374 + 13.5 = 20.933034374 x = 20.933034374 Simplifying x = 20.933034374Subproblem 2
x + -13.5 = -7.433034374 Simplifying x + -13.5 = -7.433034374 Reorder the terms: -13.5 + x = -7.433034374 Solving -13.5 + x = -7.433034374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = -7.433034374 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = -7.433034374 + 13.5 x = -7.433034374 + 13.5 Combine like terms: -7.433034374 + 13.5 = 6.066965626 x = 6.066965626 Simplifying x = 6.066965626Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.933034374, 6.066965626}
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