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Simplifying (5x + -5)(x + -1) = 60x + -185 Reorder the terms: (-5 + 5x)(x + -1) = 60x + -185 Reorder the terms: (-5 + 5x)(-1 + x) = 60x + -185 Multiply (-5 + 5x) * (-1 + x) (-5(-1 + x) + 5x * (-1 + x)) = 60x + -185 ((-1 * -5 + x * -5) + 5x * (-1 + x)) = 60x + -185 ((5 + -5x) + 5x * (-1 + x)) = 60x + -185 (5 + -5x + (-1 * 5x + x * 5x)) = 60x + -185 (5 + -5x + (-5x + 5x2)) = 60x + -185 Combine like terms: -5x + -5x = -10x (5 + -10x + 5x2) = 60x + -185 Reorder the terms: 5 + -10x + 5x2 = -185 + 60x Solving 5 + -10x + 5x2 = -185 + 60x Solving for variable 'x'. Reorder the terms: 5 + 185 + -10x + -60x + 5x2 = -185 + 60x + 185 + -60x Combine like terms: 5 + 185 = 190 190 + -10x + -60x + 5x2 = -185 + 60x + 185 + -60x Combine like terms: -10x + -60x = -70x 190 + -70x + 5x2 = -185 + 60x + 185 + -60x Reorder the terms: 190 + -70x + 5x2 = -185 + 185 + 60x + -60x Combine like terms: -185 + 185 = 0 190 + -70x + 5x2 = 0 + 60x + -60x 190 + -70x + 5x2 = 60x + -60x Combine like terms: 60x + -60x = 0 190 + -70x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(38 + -14x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(38 + -14x + x2)' equal to zero and attempt to solve: Simplifying 38 + -14x + x2 = 0 Solving 38 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-38' to each side of the equation. 38 + -14x + -38 + x2 = 0 + -38 Reorder the terms: 38 + -38 + -14x + x2 = 0 + -38 Combine like terms: 38 + -38 = 0 0 + -14x + x2 = 0 + -38 -14x + x2 = 0 + -38 Combine like terms: 0 + -38 = -38 -14x + x2 = -38 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -38 + 49 Reorder the terms: 49 + -14x + x2 = -38 + 49 Combine like terms: -38 + 49 = 11 49 + -14x + x2 = 11 Factor a perfect square on the left side: (x + -7)(x + -7) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + -7) equal to 3.31662479 and -3.31662479.Subproblem 1
x + -7 = 3.31662479 Simplifying x + -7 = 3.31662479 Reorder the terms: -7 + x = 3.31662479 Solving -7 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 3.31662479 + 7 Combine like terms: -7 + 7 = 0 0 + x = 3.31662479 + 7 x = 3.31662479 + 7 Combine like terms: 3.31662479 + 7 = 10.31662479 x = 10.31662479 Simplifying x = 10.31662479Subproblem 2
x + -7 = -3.31662479 Simplifying x + -7 = -3.31662479 Reorder the terms: -7 + x = -3.31662479 Solving -7 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -3.31662479 + 7 Combine like terms: -7 + 7 = 0 0 + x = -3.31662479 + 7 x = -3.31662479 + 7 Combine like terms: -3.31662479 + 7 = 3.68337521 x = 3.68337521 Simplifying x = 3.68337521Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.31662479, 3.68337521}Solution
x = {10.31662479, 3.68337521}
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