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Simplifying (5x + -7)(x + 5) = 23 Reorder the terms: (-7 + 5x)(x + 5) = 23 Reorder the terms: (-7 + 5x)(5 + x) = 23 Multiply (-7 + 5x) * (5 + x) (-7(5 + x) + 5x * (5 + x)) = 23 ((5 * -7 + x * -7) + 5x * (5 + x)) = 23 ((-35 + -7x) + 5x * (5 + x)) = 23 (-35 + -7x + (5 * 5x + x * 5x)) = 23 (-35 + -7x + (25x + 5x2)) = 23 Combine like terms: -7x + 25x = 18x (-35 + 18x + 5x2) = 23 Solving -35 + 18x + 5x2 = 23 Solving for variable 'x'. Reorder the terms: -35 + -23 + 18x + 5x2 = 23 + -23 Combine like terms: -35 + -23 = -58 -58 + 18x + 5x2 = 23 + -23 Combine like terms: 23 + -23 = 0 -58 + 18x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -11.6 + 3.6x + x2 = 0 Move the constant term to the right: Add '11.6' to each side of the equation. -11.6 + 3.6x + 11.6 + x2 = 0 + 11.6 Reorder the terms: -11.6 + 11.6 + 3.6x + x2 = 0 + 11.6 Combine like terms: -11.6 + 11.6 = 0.0 0.0 + 3.6x + x2 = 0 + 11.6 3.6x + x2 = 0 + 11.6 Combine like terms: 0 + 11.6 = 11.6 3.6x + x2 = 11.6 The x term is 3.6x. Take half its coefficient (1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. 3.6x + 3.24 + x2 = 11.6 + 3.24 Reorder the terms: 3.24 + 3.6x + x2 = 11.6 + 3.24 Combine like terms: 11.6 + 3.24 = 14.84 3.24 + 3.6x + x2 = 14.84 Factor a perfect square on the left side: (x + 1.8)(x + 1.8) = 14.84 Calculate the square root of the right side: 3.852272057 Break this problem into two subproblems by setting (x + 1.8) equal to 3.852272057 and -3.852272057.Subproblem 1
x + 1.8 = 3.852272057 Simplifying x + 1.8 = 3.852272057 Reorder the terms: 1.8 + x = 3.852272057 Solving 1.8 + x = 3.852272057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = 3.852272057 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = 3.852272057 + -1.8 x = 3.852272057 + -1.8 Combine like terms: 3.852272057 + -1.8 = 2.052272057 x = 2.052272057 Simplifying x = 2.052272057Subproblem 2
x + 1.8 = -3.852272057 Simplifying x + 1.8 = -3.852272057 Reorder the terms: 1.8 + x = -3.852272057 Solving 1.8 + x = -3.852272057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = -3.852272057 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = -3.852272057 + -1.8 x = -3.852272057 + -1.8 Combine like terms: -3.852272057 + -1.8 = -5.652272057 x = -5.652272057 Simplifying x = -5.652272057Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.052272057, -5.652272057}
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