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Simplifying (3x + 8)(6x + 7) + -1(2x + -1)(5x + -4) = 0 Reorder the terms: (8 + 3x)(6x + 7) + -1(2x + -1)(5x + -4) = 0 Reorder the terms: (8 + 3x)(7 + 6x) + -1(2x + -1)(5x + -4) = 0 Multiply (8 + 3x) * (7 + 6x) (8(7 + 6x) + 3x * (7 + 6x)) + -1(2x + -1)(5x + -4) = 0 ((7 * 8 + 6x * 8) + 3x * (7 + 6x)) + -1(2x + -1)(5x + -4) = 0 ((56 + 48x) + 3x * (7 + 6x)) + -1(2x + -1)(5x + -4) = 0 (56 + 48x + (7 * 3x + 6x * 3x)) + -1(2x + -1)(5x + -4) = 0 (56 + 48x + (21x + 18x2)) + -1(2x + -1)(5x + -4) = 0 Combine like terms: 48x + 21x = 69x (56 + 69x + 18x2) + -1(2x + -1)(5x + -4) = 0 Reorder the terms: 56 + 69x + 18x2 + -1(-1 + 2x)(5x + -4) = 0 Reorder the terms: 56 + 69x + 18x2 + -1(-1 + 2x)(-4 + 5x) = 0 Multiply (-1 + 2x) * (-4 + 5x) 56 + 69x + 18x2 + -1(-1(-4 + 5x) + 2x * (-4 + 5x)) = 0 56 + 69x + 18x2 + -1((-4 * -1 + 5x * -1) + 2x * (-4 + 5x)) = 0 56 + 69x + 18x2 + -1((4 + -5x) + 2x * (-4 + 5x)) = 0 56 + 69x + 18x2 + -1(4 + -5x + (-4 * 2x + 5x * 2x)) = 0 56 + 69x + 18x2 + -1(4 + -5x + (-8x + 10x2)) = 0 Combine like terms: -5x + -8x = -13x 56 + 69x + 18x2 + -1(4 + -13x + 10x2) = 0 56 + 69x + 18x2 + (4 * -1 + -13x * -1 + 10x2 * -1) = 0 56 + 69x + 18x2 + (-4 + 13x + -10x2) = 0 Reorder the terms: 56 + -4 + 69x + 13x + 18x2 + -10x2 = 0 Combine like terms: 56 + -4 = 52 52 + 69x + 13x + 18x2 + -10x2 = 0 Combine like terms: 69x + 13x = 82x 52 + 82x + 18x2 + -10x2 = 0 Combine like terms: 18x2 + -10x2 = 8x2 52 + 82x + 8x2 = 0 Solving 52 + 82x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(26 + 41x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(26 + 41x + 4x2)' equal to zero and attempt to solve: Simplifying 26 + 41x + 4x2 = 0 Solving 26 + 41x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6.5 + 10.25x + x2 = 0 Move the constant term to the right: Add '-6.5' to each side of the equation. 6.5 + 10.25x + -6.5 + x2 = 0 + -6.5 Reorder the terms: 6.5 + -6.5 + 10.25x + x2 = 0 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + 10.25x + x2 = 0 + -6.5 10.25x + x2 = 0 + -6.5 Combine like terms: 0 + -6.5 = -6.5 10.25x + x2 = -6.5 The x term is 10.25x. Take half its coefficient (5.125). Square it (26.265625) and add it to both sides. Add '26.265625' to each side of the equation. 10.25x + 26.265625 + x2 = -6.5 + 26.265625 Reorder the terms: 26.265625 + 10.25x + x2 = -6.5 + 26.265625 Combine like terms: -6.5 + 26.265625 = 19.765625 26.265625 + 10.25x + x2 = 19.765625 Factor a perfect square on the left side: (x + 5.125)(x + 5.125) = 19.765625 Calculate the square root of the right side: 4.445854811 Break this problem into two subproblems by setting (x + 5.125) equal to 4.445854811 and -4.445854811.Subproblem 1
x + 5.125 = 4.445854811 Simplifying x + 5.125 = 4.445854811 Reorder the terms: 5.125 + x = 4.445854811 Solving 5.125 + x = 4.445854811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.125' to each side of the equation. 5.125 + -5.125 + x = 4.445854811 + -5.125 Combine like terms: 5.125 + -5.125 = 0.000 0.000 + x = 4.445854811 + -5.125 x = 4.445854811 + -5.125 Combine like terms: 4.445854811 + -5.125 = -0.679145189 x = -0.679145189 Simplifying x = -0.679145189Subproblem 2
x + 5.125 = -4.445854811 Simplifying x + 5.125 = -4.445854811 Reorder the terms: 5.125 + x = -4.445854811 Solving 5.125 + x = -4.445854811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.125' to each side of the equation. 5.125 + -5.125 + x = -4.445854811 + -5.125 Combine like terms: 5.125 + -5.125 = 0.000 0.000 + x = -4.445854811 + -5.125 x = -4.445854811 + -5.125 Combine like terms: -4.445854811 + -5.125 = -9.570854811 x = -9.570854811 Simplifying x = -9.570854811Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.679145189, -9.570854811}Solution
x = {-0.679145189, -9.570854811}
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