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Simplifying (x + -12)(x + -12) = 17 Reorder the terms: (-12 + x)(x + -12) = 17 Reorder the terms: (-12 + x)(-12 + x) = 17 Multiply (-12 + x) * (-12 + x) (-12(-12 + x) + x(-12 + x)) = 17 ((-12 * -12 + x * -12) + x(-12 + x)) = 17 ((144 + -12x) + x(-12 + x)) = 17 (144 + -12x + (-12 * x + x * x)) = 17 (144 + -12x + (-12x + x2)) = 17 Combine like terms: -12x + -12x = -24x (144 + -24x + x2) = 17 Solving 144 + -24x + x2 = 17 Solving for variable 'x'. Reorder the terms: 144 + -17 + -24x + x2 = 17 + -17 Combine like terms: 144 + -17 = 127 127 + -24x + x2 = 17 + -17 Combine like terms: 17 + -17 = 0 127 + -24x + x2 = 0 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 = 16.123105626 x = 16.123105626 Simplifying x = 16.123105626Subproblem 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 = 7.876894374 x = 7.876894374 Simplifying x = 7.876894374Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.123105626, 7.876894374}
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