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Simplifying (4x + 3)(x + -2) = 9 Reorder the terms: (3 + 4x)(x + -2) = 9 Reorder the terms: (3 + 4x)(-2 + x) = 9 Multiply (3 + 4x) * (-2 + x) (3(-2 + x) + 4x * (-2 + x)) = 9 ((-2 * 3 + x * 3) + 4x * (-2 + x)) = 9 ((-6 + 3x) + 4x * (-2 + x)) = 9 (-6 + 3x + (-2 * 4x + x * 4x)) = 9 (-6 + 3x + (-8x + 4x2)) = 9 Combine like terms: 3x + -8x = -5x (-6 + -5x + 4x2) = 9 Solving -6 + -5x + 4x2 = 9 Solving for variable 'x'. Reorder the terms: -6 + -9 + -5x + 4x2 = 9 + -9 Combine like terms: -6 + -9 = -15 -15 + -5x + 4x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -15 + -5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + -1.25x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -1.25x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -1.25x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -1.25x + x2 = 0 + 3.75 -1.25x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -1.25x + x2 = 3.75 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = 3.75 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 3.75 + 0.390625 Combine like terms: 3.75 + 0.390625 = 4.140625 0.390625 + -1.25x + x2 = 4.140625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 4.140625 Calculate the square root of the right side: 2.034852575 Break this problem into two subproblems by setting (x + -0.625) equal to 2.034852575 and -2.034852575.Subproblem 1
x + -0.625 = 2.034852575 Simplifying x + -0.625 = 2.034852575 Reorder the terms: -0.625 + x = 2.034852575 Solving -0.625 + x = 2.034852575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 2.034852575 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 2.034852575 + 0.625 x = 2.034852575 + 0.625 Combine like terms: 2.034852575 + 0.625 = 2.659852575 x = 2.659852575 Simplifying x = 2.659852575Subproblem 2
x + -0.625 = -2.034852575 Simplifying x + -0.625 = -2.034852575 Reorder the terms: -0.625 + x = -2.034852575 Solving -0.625 + x = -2.034852575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -2.034852575 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -2.034852575 + 0.625 x = -2.034852575 + 0.625 Combine like terms: -2.034852575 + 0.625 = -1.409852575 x = -1.409852575 Simplifying x = -1.409852575Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.659852575, -1.409852575}
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