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Simplifying (5x + -8)(3x + 4) = 140 Reorder the terms: (-8 + 5x)(3x + 4) = 140 Reorder the terms: (-8 + 5x)(4 + 3x) = 140 Multiply (-8 + 5x) * (4 + 3x) (-8(4 + 3x) + 5x * (4 + 3x)) = 140 ((4 * -8 + 3x * -8) + 5x * (4 + 3x)) = 140 ((-32 + -24x) + 5x * (4 + 3x)) = 140 (-32 + -24x + (4 * 5x + 3x * 5x)) = 140 (-32 + -24x + (20x + 15x2)) = 140 Combine like terms: -24x + 20x = -4x (-32 + -4x + 15x2) = 140 Solving -32 + -4x + 15x2 = 140 Solving for variable 'x'. Reorder the terms: -32 + -140 + -4x + 15x2 = 140 + -140 Combine like terms: -32 + -140 = -172 -172 + -4x + 15x2 = 140 + -140 Combine like terms: 140 + -140 = 0 -172 + -4x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -11.46666667 + -0.2666666667x + x2 = 0 Move the constant term to the right: Add '11.46666667' to each side of the equation. -11.46666667 + -0.2666666667x + 11.46666667 + x2 = 0 + 11.46666667 Reorder the terms: -11.46666667 + 11.46666667 + -0.2666666667x + x2 = 0 + 11.46666667 Combine like terms: -11.46666667 + 11.46666667 = 0.00000000 0.00000000 + -0.2666666667x + x2 = 0 + 11.46666667 -0.2666666667x + x2 = 0 + 11.46666667 Combine like terms: 0 + 11.46666667 = 11.46666667 -0.2666666667x + x2 = 11.46666667 The x term is -0.2666666667x. Take half its coefficient (-0.1333333334). Square it (0.01777777780) and add it to both sides. Add '0.01777777780' to each side of the equation. -0.2666666667x + 0.01777777780 + x2 = 11.46666667 + 0.01777777780 Reorder the terms: 0.01777777780 + -0.2666666667x + x2 = 11.46666667 + 0.01777777780 Combine like terms: 11.46666667 + 0.01777777780 = 11.4844444478 0.01777777780 + -0.2666666667x + x2 = 11.4844444478 Factor a perfect square on the left side: (x + -0.1333333334)(x + -0.1333333334) = 11.4844444478 Calculate the square root of the right side: 3.388870674 Break this problem into two subproblems by setting (x + -0.1333333334) equal to 3.388870674 and -3.388870674.Subproblem 1
x + -0.1333333334 = 3.388870674 Simplifying x + -0.1333333334 = 3.388870674 Reorder the terms: -0.1333333334 + x = 3.388870674 Solving -0.1333333334 + x = 3.388870674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1333333334' to each side of the equation. -0.1333333334 + 0.1333333334 + x = 3.388870674 + 0.1333333334 Combine like terms: -0.1333333334 + 0.1333333334 = 0.0000000000 0.0000000000 + x = 3.388870674 + 0.1333333334 x = 3.388870674 + 0.1333333334 Combine like terms: 3.388870674 + 0.1333333334 = 3.5222040074 x = 3.5222040074 Simplifying x = 3.5222040074Subproblem 2
x + -0.1333333334 = -3.388870674 Simplifying x + -0.1333333334 = -3.388870674 Reorder the terms: -0.1333333334 + x = -3.388870674 Solving -0.1333333334 + x = -3.388870674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1333333334' to each side of the equation. -0.1333333334 + 0.1333333334 + x = -3.388870674 + 0.1333333334 Combine like terms: -0.1333333334 + 0.1333333334 = 0.0000000000 0.0000000000 + x = -3.388870674 + 0.1333333334 x = -3.388870674 + 0.1333333334 Combine like terms: -3.388870674 + 0.1333333334 = -3.2555373406 x = -3.2555373406 Simplifying x = -3.2555373406Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.5222040074, -3.2555373406}
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