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Simplifying 11x + x(x + -12) = 112 Reorder the terms: 11x + x(-12 + x) = 112 11x + (-12 * x + x * x) = 112 11x + (-12x + x2) = 112 Combine like terms: 11x + -12x = -1x -1x + x2 = 112 Solving -1x + x2 = 112 Solving for variable 'x'. Reorder the terms: -112 + -1x + x2 = 112 + -112 Combine like terms: 112 + -112 = 0 -112 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '112' to each side of the equation. -112 + -1x + 112 + x2 = 0 + 112 Reorder the terms: -112 + 112 + -1x + x2 = 0 + 112 Combine like terms: -112 + 112 = 0 0 + -1x + x2 = 0 + 112 -1x + x2 = 0 + 112 Combine like terms: 0 + 112 = 112 -1x + x2 = 112 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 112 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 112 + 0.25 Combine like terms: 112 + 0.25 = 112.25 0.25 + -1x + x2 = 112.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 112.25 Calculate the square root of the right side: 10.59481005 Break this problem into two subproblems by setting (x + -0.5) equal to 10.59481005 and -10.59481005.Subproblem 1
x + -0.5 = 10.59481005 Simplifying x + -0.5 = 10.59481005 Reorder the terms: -0.5 + x = 10.59481005 Solving -0.5 + x = 10.59481005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 10.59481005 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 10.59481005 + 0.5 x = 10.59481005 + 0.5 Combine like terms: 10.59481005 + 0.5 = 11.09481005 x = 11.09481005 Simplifying x = 11.09481005Subproblem 2
x + -0.5 = -10.59481005 Simplifying x + -0.5 = -10.59481005 Reorder the terms: -0.5 + x = -10.59481005 Solving -0.5 + x = -10.59481005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -10.59481005 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -10.59481005 + 0.5 x = -10.59481005 + 0.5 Combine like terms: -10.59481005 + 0.5 = -10.09481005 x = -10.09481005 Simplifying x = -10.09481005Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.09481005, -10.09481005}
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