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Simplifying (6x + -7)(4 + 3x) + -1(5)(7) = (5x + 78)(28) Reorder the terms: (-7 + 6x)(4 + 3x) + -1(5)(7) = (5x + 78)(28) Multiply (-7 + 6x) * (4 + 3x) (-7(4 + 3x) + 6x * (4 + 3x)) + -1(5)(7) = (5x + 78)(28) ((4 * -7 + 3x * -7) + 6x * (4 + 3x)) + -1(5)(7) = (5x + 78)(28) ((-28 + -21x) + 6x * (4 + 3x)) + -1(5)(7) = (5x + 78)(28) (-28 + -21x + (4 * 6x + 3x * 6x)) + -1(5)(7) = (5x + 78)(28) (-28 + -21x + (24x + 18x2)) + -1(5)(7) = (5x + 78)(28) Combine like terms: -21x + 24x = 3x (-28 + 3x + 18x2) + -1(5)(7) = (5x + 78)(28) Multiply -1 * 5 -28 + 3x + 18x2 + -5 * 7 = (5x + 78)(28) Multiply -5 * 7 -28 + 3x + 18x2 + -35 = (5x + 78)(28) Reorder the terms: -28 + -35 + 3x + 18x2 = (5x + 78)(28) Combine like terms: -28 + -35 = -63 -63 + 3x + 18x2 = (5x + 78)(28) Reorder the terms: -63 + 3x + 18x2 = (78 + 5x)(28) Reorder the terms for easier multiplication: -63 + 3x + 18x2 = 28(78 + 5x) -63 + 3x + 18x2 = (78 * 28 + 5x * 28) -63 + 3x + 18x2 = (2184 + 140x) Solving -63 + 3x + 18x2 = 2184 + 140x Solving for variable 'x'. Reorder the terms: -63 + -2184 + 3x + -140x + 18x2 = 2184 + 140x + -2184 + -140x Combine like terms: -63 + -2184 = -2247 -2247 + 3x + -140x + 18x2 = 2184 + 140x + -2184 + -140x Combine like terms: 3x + -140x = -137x -2247 + -137x + 18x2 = 2184 + 140x + -2184 + -140x Reorder the terms: -2247 + -137x + 18x2 = 2184 + -2184 + 140x + -140x Combine like terms: 2184 + -2184 = 0 -2247 + -137x + 18x2 = 0 + 140x + -140x -2247 + -137x + 18x2 = 140x + -140x Combine like terms: 140x + -140x = 0 -2247 + -137x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -124.8333333 + -7.611111111x + x2 = 0 Move the constant term to the right: Add '124.8333333' to each side of the equation. -124.8333333 + -7.611111111x + 124.8333333 + x2 = 0 + 124.8333333 Reorder the terms: -124.8333333 + 124.8333333 + -7.611111111x + x2 = 0 + 124.8333333 Combine like terms: -124.8333333 + 124.8333333 = 0.0000000 0.0000000 + -7.611111111x + x2 = 0 + 124.8333333 -7.611111111x + x2 = 0 + 124.8333333 Combine like terms: 0 + 124.8333333 = 124.8333333 -7.611111111x + x2 = 124.8333333 The x term is -7.611111111x. Take half its coefficient (-3.805555556). Square it (14.48225309) and add it to both sides. Add '14.48225309' to each side of the equation. -7.611111111x + 14.48225309 + x2 = 124.8333333 + 14.48225309 Reorder the terms: 14.48225309 + -7.611111111x + x2 = 124.8333333 + 14.48225309 Combine like terms: 124.8333333 + 14.48225309 = 139.31558639 14.48225309 + -7.611111111x + x2 = 139.31558639 Factor a perfect square on the left side: (x + -3.805555556)(x + -3.805555556) = 139.31558639 Calculate the square root of the right side: 11.803202379 Break this problem into two subproblems by setting (x + -3.805555556) equal to 11.803202379 and -11.803202379.Subproblem 1
x + -3.805555556 = 11.803202379 Simplifying x + -3.805555556 = 11.803202379 Reorder the terms: -3.805555556 + x = 11.803202379 Solving -3.805555556 + x = 11.803202379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.805555556' to each side of the equation. -3.805555556 + 3.805555556 + x = 11.803202379 + 3.805555556 Combine like terms: -3.805555556 + 3.805555556 = 0.000000000 0.000000000 + x = 11.803202379 + 3.805555556 x = 11.803202379 + 3.805555556 Combine like terms: 11.803202379 + 3.805555556 = 15.608757935 x = 15.608757935 Simplifying x = 15.608757935Subproblem 2
x + -3.805555556 = -11.803202379 Simplifying x + -3.805555556 = -11.803202379 Reorder the terms: -3.805555556 + x = -11.803202379 Solving -3.805555556 + x = -11.803202379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.805555556' to each side of the equation. -3.805555556 + 3.805555556 + x = -11.803202379 + 3.805555556 Combine like terms: -3.805555556 + 3.805555556 = 0.000000000 0.000000000 + x = -11.803202379 + 3.805555556 x = -11.803202379 + 3.805555556 Combine like terms: -11.803202379 + 3.805555556 = -7.997646823 x = -7.997646823 Simplifying x = -7.997646823Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.608757935, -7.997646823}
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