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Simplifying -1x(x + -12) + 2(x + 3) = x + 13 Reorder the terms: -1x(-12 + x) + 2(x + 3) = x + 13 (-12 * -1x + x * -1x) + 2(x + 3) = x + 13 (12x + -1x2) + 2(x + 3) = x + 13 Reorder the terms: 12x + -1x2 + 2(3 + x) = x + 13 12x + -1x2 + (3 * 2 + x * 2) = x + 13 12x + -1x2 + (6 + 2x) = x + 13 Reorder the terms: 6 + 12x + 2x + -1x2 = x + 13 Combine like terms: 12x + 2x = 14x 6 + 14x + -1x2 = x + 13 Reorder the terms: 6 + 14x + -1x2 = 13 + x Solving 6 + 14x + -1x2 = 13 + x Solving for variable 'x'. Reorder the terms: 6 + -13 + 14x + -1x + -1x2 = 13 + x + -13 + -1x Combine like terms: 6 + -13 = -7 -7 + 14x + -1x + -1x2 = 13 + x + -13 + -1x Combine like terms: 14x + -1x = 13x -7 + 13x + -1x2 = 13 + x + -13 + -1x Reorder the terms: -7 + 13x + -1x2 = 13 + -13 + x + -1x Combine like terms: 13 + -13 = 0 -7 + 13x + -1x2 = 0 + x + -1x -7 + 13x + -1x2 = x + -1x Combine like terms: x + -1x = 0 -7 + 13x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 7 + -13x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -13x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -13x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -13x + x2 = 0 + -7 -13x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -13x + x2 = -7 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = -7 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -7 + 42.25 Combine like terms: -7 + 42.25 = 35.25 42.25 + -13x + x2 = 35.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 35.25 Calculate the square root of the right side: 5.937171044 Break this problem into two subproblems by setting (x + -6.5) equal to 5.937171044 and -5.937171044.Subproblem 1
x + -6.5 = 5.937171044 Simplifying x + -6.5 = 5.937171044 Reorder the terms: -6.5 + x = 5.937171044 Solving -6.5 + x = 5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 5.937171044 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 5.937171044 + 6.5 x = 5.937171044 + 6.5 Combine like terms: 5.937171044 + 6.5 = 12.437171044 x = 12.437171044 Simplifying x = 12.437171044Subproblem 2
x + -6.5 = -5.937171044 Simplifying x + -6.5 = -5.937171044 Reorder the terms: -6.5 + x = -5.937171044 Solving -6.5 + x = -5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -5.937171044 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -5.937171044 + 6.5 x = -5.937171044 + 6.5 Combine like terms: -5.937171044 + 6.5 = 0.562828956 x = 0.562828956 Simplifying x = 0.562828956Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.437171044, 0.562828956}
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