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Simplifying -4(5 + -3x) + 2x = (8x + -3)(3x + -10) (5 * -4 + -3x * -4) + 2x = (8x + -3)(3x + -10) (-20 + 12x) + 2x = (8x + -3)(3x + -10) Combine like terms: 12x + 2x = 14x -20 + 14x = (8x + -3)(3x + -10) Reorder the terms: -20 + 14x = (-3 + 8x)(3x + -10) Reorder the terms: -20 + 14x = (-3 + 8x)(-10 + 3x) Multiply (-3 + 8x) * (-10 + 3x) -20 + 14x = (-3(-10 + 3x) + 8x * (-10 + 3x)) -20 + 14x = ((-10 * -3 + 3x * -3) + 8x * (-10 + 3x)) -20 + 14x = ((30 + -9x) + 8x * (-10 + 3x)) -20 + 14x = (30 + -9x + (-10 * 8x + 3x * 8x)) -20 + 14x = (30 + -9x + (-80x + 24x2)) Combine like terms: -9x + -80x = -89x -20 + 14x = (30 + -89x + 24x2) Solving -20 + 14x = 30 + -89x + 24x2 Solving for variable 'x'. Reorder the terms: -20 + -30 + 14x + 89x + -24x2 = 30 + -89x + 24x2 + -30 + 89x + -24x2 Combine like terms: -20 + -30 = -50 -50 + 14x + 89x + -24x2 = 30 + -89x + 24x2 + -30 + 89x + -24x2 Combine like terms: 14x + 89x = 103x -50 + 103x + -24x2 = 30 + -89x + 24x2 + -30 + 89x + -24x2 Reorder the terms: -50 + 103x + -24x2 = 30 + -30 + -89x + 89x + 24x2 + -24x2 Combine like terms: 30 + -30 = 0 -50 + 103x + -24x2 = 0 + -89x + 89x + 24x2 + -24x2 -50 + 103x + -24x2 = -89x + 89x + 24x2 + -24x2 Combine like terms: -89x + 89x = 0 -50 + 103x + -24x2 = 0 + 24x2 + -24x2 -50 + 103x + -24x2 = 24x2 + -24x2 Combine like terms: 24x2 + -24x2 = 0 -50 + 103x + -24x2 = 0 Begin completing the square. Divide all terms by -24 the coefficient of the squared term: Divide each side by '-24'. 2.083333333 + -4.291666667x + x2 = 0 Move the constant term to the right: Add '-2.083333333' to each side of the equation. 2.083333333 + -4.291666667x + -2.083333333 + x2 = 0 + -2.083333333 Reorder the terms: 2.083333333 + -2.083333333 + -4.291666667x + x2 = 0 + -2.083333333 Combine like terms: 2.083333333 + -2.083333333 = 0.000000000 0.000000000 + -4.291666667x + x2 = 0 + -2.083333333 -4.291666667x + x2 = 0 + -2.083333333 Combine like terms: 0 + -2.083333333 = -2.083333333 -4.291666667x + x2 = -2.083333333 The x term is -4.291666667x. Take half its coefficient (-2.145833334). Square it (4.604600697) and add it to both sides. Add '4.604600697' to each side of the equation. -4.291666667x + 4.604600697 + x2 = -2.083333333 + 4.604600697 Reorder the terms: 4.604600697 + -4.291666667x + x2 = -2.083333333 + 4.604600697 Combine like terms: -2.083333333 + 4.604600697 = 2.521267364 4.604600697 + -4.291666667x + x2 = 2.521267364 Factor a perfect square on the left side: (x + -2.145833334)(x + -2.145833334) = 2.521267364 Calculate the square root of the right side: 1.587849919 Break this problem into two subproblems by setting (x + -2.145833334) equal to 1.587849919 and -1.587849919.Subproblem 1
x + -2.145833334 = 1.587849919 Simplifying x + -2.145833334 = 1.587849919 Reorder the terms: -2.145833334 + x = 1.587849919 Solving -2.145833334 + x = 1.587849919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.145833334' to each side of the equation. -2.145833334 + 2.145833334 + x = 1.587849919 + 2.145833334 Combine like terms: -2.145833334 + 2.145833334 = 0.000000000 0.000000000 + x = 1.587849919 + 2.145833334 x = 1.587849919 + 2.145833334 Combine like terms: 1.587849919 + 2.145833334 = 3.733683253 x = 3.733683253 Simplifying x = 3.733683253Subproblem 2
x + -2.145833334 = -1.587849919 Simplifying x + -2.145833334 = -1.587849919 Reorder the terms: -2.145833334 + x = -1.587849919 Solving -2.145833334 + x = -1.587849919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.145833334' to each side of the equation. -2.145833334 + 2.145833334 + x = -1.587849919 + 2.145833334 Combine like terms: -2.145833334 + 2.145833334 = 0.000000000 0.000000000 + x = -1.587849919 + 2.145833334 x = -1.587849919 + 2.145833334 Combine like terms: -1.587849919 + 2.145833334 = 0.557983415 x = 0.557983415 Simplifying x = 0.557983415Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.733683253, 0.557983415}
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