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Simplifying 8(x + -5) * 6x = 7(2x + 4) + -13 Reorder the terms: 8(-5 + x) * 6x = 7(2x + 4) + -13 Reorder the terms for easier multiplication: 8 * 6x(-5 + x) = 7(2x + 4) + -13 Multiply 8 * 6 48x(-5 + x) = 7(2x + 4) + -13 (-5 * 48x + x * 48x) = 7(2x + 4) + -13 (-240x + 48x2) = 7(2x + 4) + -13 Reorder the terms: -240x + 48x2 = 7(4 + 2x) + -13 -240x + 48x2 = (4 * 7 + 2x * 7) + -13 -240x + 48x2 = (28 + 14x) + -13 Reorder the terms: -240x + 48x2 = 28 + -13 + 14x Combine like terms: 28 + -13 = 15 -240x + 48x2 = 15 + 14x Solving -240x + 48x2 = 15 + 14x Solving for variable 'x'. Reorder the terms: -15 + -240x + -14x + 48x2 = 15 + 14x + -15 + -14x Combine like terms: -240x + -14x = -254x -15 + -254x + 48x2 = 15 + 14x + -15 + -14x Reorder the terms: -15 + -254x + 48x2 = 15 + -15 + 14x + -14x Combine like terms: 15 + -15 = 0 -15 + -254x + 48x2 = 0 + 14x + -14x -15 + -254x + 48x2 = 14x + -14x Combine like terms: 14x + -14x = 0 -15 + -254x + 48x2 = 0 Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. -0.3125 + -5.291666667x + x2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -5.291666667x + 0.3125 + x2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -5.291666667x + x2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -5.291666667x + x2 = 0 + 0.3125 -5.291666667x + x2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -5.291666667x + x2 = 0.3125 The x term is -5.291666667x. Take half its coefficient (-2.645833334). Square it (7.000434031) and add it to both sides. Add '7.000434031' to each side of the equation. -5.291666667x + 7.000434031 + x2 = 0.3125 + 7.000434031 Reorder the terms: 7.000434031 + -5.291666667x + x2 = 0.3125 + 7.000434031 Combine like terms: 0.3125 + 7.000434031 = 7.312934031 7.000434031 + -5.291666667x + x2 = 7.312934031 Factor a perfect square on the left side: (x + -2.645833334)(x + -2.645833334) = 7.312934031 Calculate the square root of the right side: 2.704243708 Break this problem into two subproblems by setting (x + -2.645833334) equal to 2.704243708 and -2.704243708.Subproblem 1
x + -2.645833334 = 2.704243708 Simplifying x + -2.645833334 = 2.704243708 Reorder the terms: -2.645833334 + x = 2.704243708 Solving -2.645833334 + x = 2.704243708 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.645833334' to each side of the equation. -2.645833334 + 2.645833334 + x = 2.704243708 + 2.645833334 Combine like terms: -2.645833334 + 2.645833334 = 0.000000000 0.000000000 + x = 2.704243708 + 2.645833334 x = 2.704243708 + 2.645833334 Combine like terms: 2.704243708 + 2.645833334 = 5.350077042 x = 5.350077042 Simplifying x = 5.350077042Subproblem 2
x + -2.645833334 = -2.704243708 Simplifying x + -2.645833334 = -2.704243708 Reorder the terms: -2.645833334 + x = -2.704243708 Solving -2.645833334 + x = -2.704243708 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.645833334' to each side of the equation. -2.645833334 + 2.645833334 + x = -2.704243708 + 2.645833334 Combine like terms: -2.645833334 + 2.645833334 = 0.000000000 0.000000000 + x = -2.704243708 + 2.645833334 x = -2.704243708 + 2.645833334 Combine like terms: -2.704243708 + 2.645833334 = -0.058410374 x = -0.058410374 Simplifying x = -0.058410374Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.350077042, -0.058410374}
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