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Simplifying (5x + -3)(x + -7) + -1 = 0 Reorder the terms: (-3 + 5x)(x + -7) + -1 = 0 Reorder the terms: (-3 + 5x)(-7 + x) + -1 = 0 Multiply (-3 + 5x) * (-7 + x) (-3(-7 + x) + 5x * (-7 + x)) + -1 = 0 ((-7 * -3 + x * -3) + 5x * (-7 + x)) + -1 = 0 ((21 + -3x) + 5x * (-7 + x)) + -1 = 0 (21 + -3x + (-7 * 5x + x * 5x)) + -1 = 0 (21 + -3x + (-35x + 5x2)) + -1 = 0 Combine like terms: -3x + -35x = -38x (21 + -38x + 5x2) + -1 = 0 Reorder the terms: 21 + -1 + -38x + 5x2 = 0 Combine like terms: 21 + -1 = 20 20 + -38x + 5x2 = 0 Solving 20 + -38x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 4 + -7.6x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -7.6x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -7.6x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7.6x + x2 = 0 + -4 -7.6x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -7.6x + x2 = -4 The x term is -7.6x. Take half its coefficient (-3.8). Square it (14.44) and add it to both sides. Add '14.44' to each side of the equation. -7.6x + 14.44 + x2 = -4 + 14.44 Reorder the terms: 14.44 + -7.6x + x2 = -4 + 14.44 Combine like terms: -4 + 14.44 = 10.44 14.44 + -7.6x + x2 = 10.44 Factor a perfect square on the left side: (x + -3.8)(x + -3.8) = 10.44 Calculate the square root of the right side: 3.231098884 Break this problem into two subproblems by setting (x + -3.8) equal to 3.231098884 and -3.231098884.Subproblem 1
x + -3.8 = 3.231098884 Simplifying x + -3.8 = 3.231098884 Reorder the terms: -3.8 + x = 3.231098884 Solving -3.8 + x = 3.231098884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.8' to each side of the equation. -3.8 + 3.8 + x = 3.231098884 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + x = 3.231098884 + 3.8 x = 3.231098884 + 3.8 Combine like terms: 3.231098884 + 3.8 = 7.031098884 x = 7.031098884 Simplifying x = 7.031098884Subproblem 2
x + -3.8 = -3.231098884 Simplifying x + -3.8 = -3.231098884 Reorder the terms: -3.8 + x = -3.231098884 Solving -3.8 + x = -3.231098884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.8' to each side of the equation. -3.8 + 3.8 + x = -3.231098884 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + x = -3.231098884 + 3.8 x = -3.231098884 + 3.8 Combine like terms: -3.231098884 + 3.8 = 0.568901116 x = 0.568901116 Simplifying x = 0.568901116Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.031098884, 0.568901116}
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