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Simplifying 3(x + -5) * x + -5 + x = 85 Reorder the terms: 3(-5 + x) * x + -5 + x = 85 Reorder the terms for easier multiplication: 3x(-5 + x) + -5 + x = 85 (-5 * 3x + x * 3x) + -5 + x = 85 (-15x + 3x2) + -5 + x = 85 Reorder the terms: -5 + -15x + x + 3x2 = 85 Combine like terms: -15x + x = -14x -5 + -14x + 3x2 = 85 Solving -5 + -14x + 3x2 = 85 Solving for variable 'x'. Reorder the terms: -5 + -85 + -14x + 3x2 = 85 + -85 Combine like terms: -5 + -85 = -90 -90 + -14x + 3x2 = 85 + -85 Combine like terms: 85 + -85 = 0 -90 + -14x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -30 + -4.666666667x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + -4.666666667x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -4.666666667x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -4.666666667x + x2 = 0 + 30 -4.666666667x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -4.666666667x + x2 = 30 The x term is -4.666666667x. Take half its coefficient (-2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. -4.666666667x + 5.444444448 + x2 = 30 + 5.444444448 Reorder the terms: 5.444444448 + -4.666666667x + x2 = 30 + 5.444444448 Combine like terms: 30 + 5.444444448 = 35.444444448 5.444444448 + -4.666666667x + x2 = 35.444444448 Factor a perfect square on the left side: (x + -2.333333334)(x + -2.333333334) = 35.444444448 Calculate the square root of the right side: 5.9535237 Break this problem into two subproblems by setting (x + -2.333333334) equal to 5.9535237 and -5.9535237.Subproblem 1
x + -2.333333334 = 5.9535237 Simplifying x + -2.333333334 = 5.9535237 Reorder the terms: -2.333333334 + x = 5.9535237 Solving -2.333333334 + x = 5.9535237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = 5.9535237 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = 5.9535237 + 2.333333334 x = 5.9535237 + 2.333333334 Combine like terms: 5.9535237 + 2.333333334 = 8.286857034 x = 8.286857034 Simplifying x = 8.286857034Subproblem 2
x + -2.333333334 = -5.9535237 Simplifying x + -2.333333334 = -5.9535237 Reorder the terms: -2.333333334 + x = -5.9535237 Solving -2.333333334 + x = -5.9535237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = -5.9535237 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = -5.9535237 + 2.333333334 x = -5.9535237 + 2.333333334 Combine like terms: -5.9535237 + 2.333333334 = -3.620190366 x = -3.620190366 Simplifying x = -3.620190366Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.286857034, -3.620190366}
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