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Simplifying (2x + 3)(x + -2) = 12 Reorder the terms: (3 + 2x)(x + -2) = 12 Reorder the terms: (3 + 2x)(-2 + x) = 12 Multiply (3 + 2x) * (-2 + x) (3(-2 + x) + 2x * (-2 + x)) = 12 ((-2 * 3 + x * 3) + 2x * (-2 + x)) = 12 ((-6 + 3x) + 2x * (-2 + x)) = 12 (-6 + 3x + (-2 * 2x + x * 2x)) = 12 (-6 + 3x + (-4x + 2x2)) = 12 Combine like terms: 3x + -4x = -1x (-6 + -1x + 2x2) = 12 Solving -6 + -1x + 2x2 = 12 Solving for variable 'x'. Reorder the terms: -6 + -12 + -1x + 2x2 = 12 + -12 Combine like terms: -6 + -12 = -18 -18 + -1x + 2x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -18 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9 + -0.5x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -0.5x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -0.5x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -0.5x + x2 = 0 + 9 -0.5x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -0.5x + x2 = 9 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 9 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 9 + 0.0625 Combine like terms: 9 + 0.0625 = 9.0625 0.0625 + -0.5x + x2 = 9.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 9.0625 Calculate the square root of the right side: 3.010398645 Break this problem into two subproblems by setting (x + -0.25) equal to 3.010398645 and -3.010398645.Subproblem 1
x + -0.25 = 3.010398645 Simplifying x + -0.25 = 3.010398645 Reorder the terms: -0.25 + x = 3.010398645 Solving -0.25 + x = 3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 3.010398645 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 3.010398645 + 0.25 x = 3.010398645 + 0.25 Combine like terms: 3.010398645 + 0.25 = 3.260398645 x = 3.260398645 Simplifying x = 3.260398645Subproblem 2
x + -0.25 = -3.010398645 Simplifying x + -0.25 = -3.010398645 Reorder the terms: -0.25 + x = -3.010398645 Solving -0.25 + x = -3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -3.010398645 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -3.010398645 + 0.25 x = -3.010398645 + 0.25 Combine like terms: -3.010398645 + 0.25 = -2.760398645 x = -2.760398645 Simplifying x = -2.760398645Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.260398645, -2.760398645}
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