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Simplifying (2x + 3)(x + -5) = 9 Reorder the terms: (3 + 2x)(x + -5) = 9 Reorder the terms: (3 + 2x)(-5 + x) = 9 Multiply (3 + 2x) * (-5 + x) (3(-5 + x) + 2x * (-5 + x)) = 9 ((-5 * 3 + x * 3) + 2x * (-5 + x)) = 9 ((-15 + 3x) + 2x * (-5 + x)) = 9 (-15 + 3x + (-5 * 2x + x * 2x)) = 9 (-15 + 3x + (-10x + 2x2)) = 9 Combine like terms: 3x + -10x = -7x (-15 + -7x + 2x2) = 9 Solving -15 + -7x + 2x2 = 9 Solving for variable 'x'. Reorder the terms: -15 + -9 + -7x + 2x2 = 9 + -9 Combine like terms: -15 + -9 = -24 -24 + -7x + 2x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -24 + -7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12 + -3.5x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -3.5x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -3.5x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -3.5x + x2 = 0 + 12 -3.5x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -3.5x + x2 = 12 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 12 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 12 + 3.0625 Combine like terms: 12 + 3.0625 = 15.0625 3.0625 + -3.5x + x2 = 15.0625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 15.0625 Calculate the square root of the right side: 3.881043674 Break this problem into two subproblems by setting (x + -1.75) equal to 3.881043674 and -3.881043674.Subproblem 1
x + -1.75 = 3.881043674 Simplifying x + -1.75 = 3.881043674 Reorder the terms: -1.75 + x = 3.881043674 Solving -1.75 + x = 3.881043674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 3.881043674 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 3.881043674 + 1.75 x = 3.881043674 + 1.75 Combine like terms: 3.881043674 + 1.75 = 5.631043674 x = 5.631043674 Simplifying x = 5.631043674Subproblem 2
x + -1.75 = -3.881043674 Simplifying x + -1.75 = -3.881043674 Reorder the terms: -1.75 + x = -3.881043674 Solving -1.75 + x = -3.881043674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -3.881043674 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -3.881043674 + 1.75 x = -3.881043674 + 1.75 Combine like terms: -3.881043674 + 1.75 = -2.131043674 x = -2.131043674 Simplifying x = -2.131043674Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.631043674, -2.131043674}
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