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Simplifying x2 + 24x + 127 = 0 Reorder the terms: 127 + 24x + x2 = 0 Solving 127 + 24x + 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 + 24x + -127 + x2 = 0 + -127 Reorder the terms: 127 + -127 + 24x + x2 = 0 + -127 Combine like terms: 127 + -127 = 0 0 + 24x + x2 = 0 + -127 24x + x2 = 0 + -127 Combine like terms: 0 + -127 = -127 24x + x2 = -127 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = -127 + 144 Reorder the terms: 144 + 24x + x2 = -127 + 144 Combine like terms: -127 + 144 = 17 144 + 24x + x2 = 17 Factor a perfect square on the left side: (x + 12)(x + 12) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (x + 12) equal to 4.123105626 and -4.123105626.Subproblem 1
x + 12 = 4.123105626 Simplifying x + 12 = 4.123105626 Reorder the terms: 12 + x = 4.123105626 Solving 12 + x = 4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 4.123105626 + -12 Combine like terms: 12 + -12 = 0 0 + x = 4.123105626 + -12 x = 4.123105626 + -12 Combine like terms: 4.123105626 + -12 = -7.876894374 x = -7.876894374 Simplifying x = -7.876894374Subproblem 2
x + 12 = -4.123105626 Simplifying x + 12 = -4.123105626 Reorder the terms: 12 + x = -4.123105626 Solving 12 + x = -4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -4.123105626 + -12 Combine like terms: 12 + -12 = 0 0 + x = -4.123105626 + -12 x = -4.123105626 + -12 Combine like terms: -4.123105626 + -12 = -16.123105626 x = -16.123105626 Simplifying x = -16.123105626Solution
The solution to the problem is based on the solutions from the subproblems. x = {-7.876894374, -16.123105626}
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