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Simplifying x2 + -12x + -36 + x2 = x2 + 12x + 36 Reorder the terms: -36 + -12x + x2 + x2 = x2 + 12x + 36 Combine like terms: x2 + x2 = 2x2 -36 + -12x + 2x2 = x2 + 12x + 36 Reorder the terms: -36 + -12x + 2x2 = 36 + 12x + x2 Solving -36 + -12x + 2x2 = 36 + 12x + x2 Solving for variable 'x'. Reorder the terms: -36 + -36 + -12x + -12x + 2x2 + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2 Combine like terms: -36 + -36 = -72 -72 + -12x + -12x + 2x2 + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2 Combine like terms: -12x + -12x = -24x -72 + -24x + 2x2 + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -72 + -24x + 1x2 = 36 + 12x + x2 + -36 + -12x + -1x2 Reorder the terms: -72 + -24x + 1x2 = 36 + -36 + 12x + -12x + x2 + -1x2 Combine like terms: 36 + -36 = 0 -72 + -24x + 1x2 = 0 + 12x + -12x + x2 + -1x2 -72 + -24x + 1x2 = 12x + -12x + x2 + -1x2 Combine like terms: 12x + -12x = 0 -72 + -24x + 1x2 = 0 + x2 + -1x2 -72 + -24x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -72 + -24x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + -24x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + -24x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -24x + x2 = 0 + 72 -24x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 -24x + x2 = 72 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 = 72 + 144 Reorder the terms: 144 + -24x + x2 = 72 + 144 Combine like terms: 72 + 144 = 216 144 + -24x + x2 = 216 Factor a perfect square on the left side: (x + -12)(x + -12) = 216 Calculate the square root of the right side: 14.696938457 Break this problem into two subproblems by setting (x + -12) equal to 14.696938457 and -14.696938457.Subproblem 1
x + -12 = 14.696938457 Simplifying x + -12 = 14.696938457 Reorder the terms: -12 + x = 14.696938457 Solving -12 + x = 14.696938457 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 = 14.696938457 + 12 Combine like terms: -12 + 12 = 0 0 + x = 14.696938457 + 12 x = 14.696938457 + 12 Combine like terms: 14.696938457 + 12 = 26.696938457 x = 26.696938457 Simplifying x = 26.696938457Subproblem 2
x + -12 = -14.696938457 Simplifying x + -12 = -14.696938457 Reorder the terms: -12 + x = -14.696938457 Solving -12 + x = -14.696938457 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 = -14.696938457 + 12 Combine like terms: -12 + 12 = 0 0 + x = -14.696938457 + 12 x = -14.696938457 + 12 Combine like terms: -14.696938457 + 12 = -2.696938457 x = -2.696938457 Simplifying x = -2.696938457Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.696938457, -2.696938457}
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