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Simplifying (2x + -3)(x + -12) = x Reorder the terms: (-3 + 2x)(x + -12) = x Reorder the terms: (-3 + 2x)(-12 + x) = x Multiply (-3 + 2x) * (-12 + x) (-3(-12 + x) + 2x * (-12 + x)) = x ((-12 * -3 + x * -3) + 2x * (-12 + x)) = x ((36 + -3x) + 2x * (-12 + x)) = x (36 + -3x + (-12 * 2x + x * 2x)) = x (36 + -3x + (-24x + 2x2)) = x Combine like terms: -3x + -24x = -27x (36 + -27x + 2x2) = x Solving 36 + -27x + 2x2 = x Solving for variable 'x'. Reorder the terms: 36 + -27x + -1x + 2x2 = x + -1x Combine like terms: -27x + -1x = -28x 36 + -28x + 2x2 = x + -1x Combine like terms: x + -1x = 0 36 + -28x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(18 + -14x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(18 + -14x + x2)' equal to zero and attempt to solve: Simplifying 18 + -14x + x2 = 0 Solving 18 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -14x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + -14x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -14x + x2 = 0 + -18 -14x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 -14x + x2 = -18 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -18 + 49 Reorder the terms: 49 + -14x + x2 = -18 + 49 Combine like terms: -18 + 49 = 31 49 + -14x + x2 = 31 Factor a perfect square on the left side: (x + -7)(x + -7) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (x + -7) equal to 5.567764363 and -5.567764363.Subproblem 1
x + -7 = 5.567764363 Simplifying x + -7 = 5.567764363 Reorder the terms: -7 + x = 5.567764363 Solving -7 + x = 5.567764363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 5.567764363 + 7 Combine like terms: -7 + 7 = 0 0 + x = 5.567764363 + 7 x = 5.567764363 + 7 Combine like terms: 5.567764363 + 7 = 12.567764363 x = 12.567764363 Simplifying x = 12.567764363Subproblem 2
x + -7 = -5.567764363 Simplifying x + -7 = -5.567764363 Reorder the terms: -7 + x = -5.567764363 Solving -7 + x = -5.567764363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -5.567764363 + 7 Combine like terms: -7 + 7 = 0 0 + x = -5.567764363 + 7 x = -5.567764363 + 7 Combine like terms: -5.567764363 + 7 = 1.432235637 x = 1.432235637 Simplifying x = 1.432235637Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.567764363, 1.432235637}Solution
x = {12.567764363, 1.432235637}
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