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Simplifying (2x + 5)(3x + -8) = 2x Reorder the terms: (5 + 2x)(3x + -8) = 2x Reorder the terms: (5 + 2x)(-8 + 3x) = 2x Multiply (5 + 2x) * (-8 + 3x) (5(-8 + 3x) + 2x * (-8 + 3x)) = 2x ((-8 * 5 + 3x * 5) + 2x * (-8 + 3x)) = 2x ((-40 + 15x) + 2x * (-8 + 3x)) = 2x (-40 + 15x + (-8 * 2x + 3x * 2x)) = 2x (-40 + 15x + (-16x + 6x2)) = 2x Combine like terms: 15x + -16x = -1x (-40 + -1x + 6x2) = 2x Solving -40 + -1x + 6x2 = 2x Solving for variable 'x'. Reorder the terms: -40 + -1x + -2x + 6x2 = 2x + -2x Combine like terms: -1x + -2x = -3x -40 + -3x + 6x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -40 + -3x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -6.666666667 + -0.5x + x2 = 0 Move the constant term to the right: Add '6.666666667' to each side of the equation. -6.666666667 + -0.5x + 6.666666667 + x2 = 0 + 6.666666667 Reorder the terms: -6.666666667 + 6.666666667 + -0.5x + x2 = 0 + 6.666666667 Combine like terms: -6.666666667 + 6.666666667 = 0.000000000 0.000000000 + -0.5x + x2 = 0 + 6.666666667 -0.5x + x2 = 0 + 6.666666667 Combine like terms: 0 + 6.666666667 = 6.666666667 -0.5x + x2 = 6.666666667 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 = 6.666666667 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 6.666666667 + 0.0625 Combine like terms: 6.666666667 + 0.0625 = 6.729166667 0.0625 + -0.5x + x2 = 6.729166667 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 6.729166667 Calculate the square root of the right side: 2.594063736 Break this problem into two subproblems by setting (x + -0.25) equal to 2.594063736 and -2.594063736.Subproblem 1
x + -0.25 = 2.594063736 Simplifying x + -0.25 = 2.594063736 Reorder the terms: -0.25 + x = 2.594063736 Solving -0.25 + x = 2.594063736 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 = 2.594063736 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 2.594063736 + 0.25 x = 2.594063736 + 0.25 Combine like terms: 2.594063736 + 0.25 = 2.844063736 x = 2.844063736 Simplifying x = 2.844063736Subproblem 2
x + -0.25 = -2.594063736 Simplifying x + -0.25 = -2.594063736 Reorder the terms: -0.25 + x = -2.594063736 Solving -0.25 + x = -2.594063736 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 = -2.594063736 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -2.594063736 + 0.25 x = -2.594063736 + 0.25 Combine like terms: -2.594063736 + 0.25 = -2.344063736 x = -2.344063736 Simplifying x = -2.344063736Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.844063736, -2.344063736}
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