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Simplifying 1(2x + -4) + 1(3x + 5) = 4(2x + -4)(3x + 5) Reorder the terms: 1(-4 + 2x) + 1(3x + 5) = 4(2x + -4)(3x + 5) (-4 * 1 + 2x * 1) + 1(3x + 5) = 4(2x + -4)(3x + 5) (-4 + 2x) + 1(3x + 5) = 4(2x + -4)(3x + 5) Reorder the terms: -4 + 2x + 1(5 + 3x) = 4(2x + -4)(3x + 5) -4 + 2x + (5 * 1 + 3x * 1) = 4(2x + -4)(3x + 5) -4 + 2x + (5 + 3x) = 4(2x + -4)(3x + 5) Reorder the terms: -4 + 5 + 2x + 3x = 4(2x + -4)(3x + 5) Combine like terms: -4 + 5 = 1 1 + 2x + 3x = 4(2x + -4)(3x + 5) Combine like terms: 2x + 3x = 5x 1 + 5x = 4(2x + -4)(3x + 5) Reorder the terms: 1 + 5x = 4(-4 + 2x)(3x + 5) Reorder the terms: 1 + 5x = 4(-4 + 2x)(5 + 3x) Multiply (-4 + 2x) * (5 + 3x) 1 + 5x = 4(-4(5 + 3x) + 2x * (5 + 3x)) 1 + 5x = 4((5 * -4 + 3x * -4) + 2x * (5 + 3x)) 1 + 5x = 4((-20 + -12x) + 2x * (5 + 3x)) 1 + 5x = 4(-20 + -12x + (5 * 2x + 3x * 2x)) 1 + 5x = 4(-20 + -12x + (10x + 6x2)) Combine like terms: -12x + 10x = -2x 1 + 5x = 4(-20 + -2x + 6x2) 1 + 5x = (-20 * 4 + -2x * 4 + 6x2 * 4) 1 + 5x = (-80 + -8x + 24x2) Solving 1 + 5x = -80 + -8x + 24x2 Solving for variable 'x'. Reorder the terms: 1 + 80 + 5x + 8x + -24x2 = -80 + -8x + 24x2 + 80 + 8x + -24x2 Combine like terms: 1 + 80 = 81 81 + 5x + 8x + -24x2 = -80 + -8x + 24x2 + 80 + 8x + -24x2 Combine like terms: 5x + 8x = 13x 81 + 13x + -24x2 = -80 + -8x + 24x2 + 80 + 8x + -24x2 Reorder the terms: 81 + 13x + -24x2 = -80 + 80 + -8x + 8x + 24x2 + -24x2 Combine like terms: -80 + 80 = 0 81 + 13x + -24x2 = 0 + -8x + 8x + 24x2 + -24x2 81 + 13x + -24x2 = -8x + 8x + 24x2 + -24x2 Combine like terms: -8x + 8x = 0 81 + 13x + -24x2 = 0 + 24x2 + -24x2 81 + 13x + -24x2 = 24x2 + -24x2 Combine like terms: 24x2 + -24x2 = 0 81 + 13x + -24x2 = 0 Begin completing the square. Divide all terms by -24 the coefficient of the squared term: Divide each side by '-24'. -3.375 + -0.5416666667x + x2 = 0 Move the constant term to the right: Add '3.375' to each side of the equation. -3.375 + -0.5416666667x + 3.375 + x2 = 0 + 3.375 Reorder the terms: -3.375 + 3.375 + -0.5416666667x + x2 = 0 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + -0.5416666667x + x2 = 0 + 3.375 -0.5416666667x + x2 = 0 + 3.375 Combine like terms: 0 + 3.375 = 3.375 -0.5416666667x + x2 = 3.375 The x term is -0.5416666667x. Take half its coefficient (-0.2708333334). Square it (0.07335069448) and add it to both sides. Add '0.07335069448' to each side of the equation. -0.5416666667x + 0.07335069448 + x2 = 3.375 + 0.07335069448 Reorder the terms: 0.07335069448 + -0.5416666667x + x2 = 3.375 + 0.07335069448 Combine like terms: 3.375 + 0.07335069448 = 3.44835069448 0.07335069448 + -0.5416666667x + x2 = 3.44835069448 Factor a perfect square on the left side: (x + -0.2708333334)(x + -0.2708333334) = 3.44835069448 Calculate the square root of the right side: 1.856973531 Break this problem into two subproblems by setting (x + -0.2708333334) equal to 1.856973531 and -1.856973531.Subproblem 1
x + -0.2708333334 = 1.856973531 Simplifying x + -0.2708333334 = 1.856973531 Reorder the terms: -0.2708333334 + x = 1.856973531 Solving -0.2708333334 + x = 1.856973531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2708333334' to each side of the equation. -0.2708333334 + 0.2708333334 + x = 1.856973531 + 0.2708333334 Combine like terms: -0.2708333334 + 0.2708333334 = 0.0000000000 0.0000000000 + x = 1.856973531 + 0.2708333334 x = 1.856973531 + 0.2708333334 Combine like terms: 1.856973531 + 0.2708333334 = 2.1278068644 x = 2.1278068644 Simplifying x = 2.1278068644Subproblem 2
x + -0.2708333334 = -1.856973531 Simplifying x + -0.2708333334 = -1.856973531 Reorder the terms: -0.2708333334 + x = -1.856973531 Solving -0.2708333334 + x = -1.856973531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2708333334' to each side of the equation. -0.2708333334 + 0.2708333334 + x = -1.856973531 + 0.2708333334 Combine like terms: -0.2708333334 + 0.2708333334 = 0.0000000000 0.0000000000 + x = -1.856973531 + 0.2708333334 x = -1.856973531 + 0.2708333334 Combine like terms: -1.856973531 + 0.2708333334 = -1.5861401976 x = -1.5861401976 Simplifying x = -1.5861401976Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1278068644, -1.5861401976}
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