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Simplifying (5x + 4)(6x + -7) = 50 Reorder the terms: (4 + 5x)(6x + -7) = 50 Reorder the terms: (4 + 5x)(-7 + 6x) = 50 Multiply (4 + 5x) * (-7 + 6x) (4(-7 + 6x) + 5x * (-7 + 6x)) = 50 ((-7 * 4 + 6x * 4) + 5x * (-7 + 6x)) = 50 ((-28 + 24x) + 5x * (-7 + 6x)) = 50 (-28 + 24x + (-7 * 5x + 6x * 5x)) = 50 (-28 + 24x + (-35x + 30x2)) = 50 Combine like terms: 24x + -35x = -11x (-28 + -11x + 30x2) = 50 Solving -28 + -11x + 30x2 = 50 Solving for variable 'x'. Reorder the terms: -28 + -50 + -11x + 30x2 = 50 + -50 Combine like terms: -28 + -50 = -78 -78 + -11x + 30x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -78 + -11x + 30x2 = 0 Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. -2.6 + -0.3666666667x + x2 = 0.0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + -0.3666666667x + 2.6 + x2 = 0.0 + 2.6 Reorder the terms: -2.6 + 2.6 + -0.3666666667x + x2 = 0.0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + -0.3666666667x + x2 = 0.0 + 2.6 -0.3666666667x + x2 = 0.0 + 2.6 Combine like terms: 0.0 + 2.6 = 2.6 -0.3666666667x + x2 = 2.6 The x term is -0.3666666667x. Take half its coefficient (-0.1833333334). Square it (0.03361111114) and add it to both sides. Add '0.03361111114' to each side of the equation. -0.3666666667x + 0.03361111114 + x2 = 2.6 + 0.03361111114 Reorder the terms: 0.03361111114 + -0.3666666667x + x2 = 2.6 + 0.03361111114 Combine like terms: 2.6 + 0.03361111114 = 2.63361111114 0.03361111114 + -0.3666666667x + x2 = 2.63361111114 Factor a perfect square on the left side: (x + -0.1833333334)(x + -0.1833333334) = 2.63361111114 Calculate the square root of the right side: 1.622840445 Break this problem into two subproblems by setting (x + -0.1833333334) equal to 1.622840445 and -1.622840445.Subproblem 1
x + -0.1833333334 = 1.622840445 Simplifying x + -0.1833333334 = 1.622840445 Reorder the terms: -0.1833333334 + x = 1.622840445 Solving -0.1833333334 + x = 1.622840445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1833333334' to each side of the equation. -0.1833333334 + 0.1833333334 + x = 1.622840445 + 0.1833333334 Combine like terms: -0.1833333334 + 0.1833333334 = 0.0000000000 0.0000000000 + x = 1.622840445 + 0.1833333334 x = 1.622840445 + 0.1833333334 Combine like terms: 1.622840445 + 0.1833333334 = 1.8061737784 x = 1.8061737784 Simplifying x = 1.8061737784Subproblem 2
x + -0.1833333334 = -1.622840445 Simplifying x + -0.1833333334 = -1.622840445 Reorder the terms: -0.1833333334 + x = -1.622840445 Solving -0.1833333334 + x = -1.622840445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1833333334' to each side of the equation. -0.1833333334 + 0.1833333334 + x = -1.622840445 + 0.1833333334 Combine like terms: -0.1833333334 + 0.1833333334 = 0.0000000000 0.0000000000 + x = -1.622840445 + 0.1833333334 x = -1.622840445 + 0.1833333334 Combine like terms: -1.622840445 + 0.1833333334 = -1.4395071116 x = -1.4395071116 Simplifying x = -1.4395071116Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8061737784, -1.4395071116}
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