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Simplifying 15x + 3 + -2(x + -1) = (7 + -1x)(7 + x) Reorder the terms: 15x + 3 + -2(-1 + x) = (7 + -1x)(7 + x) 15x + 3 + (-1 * -2 + x * -2) = (7 + -1x)(7 + x) 15x + 3 + (2 + -2x) = (7 + -1x)(7 + x) Reorder the terms: 3 + 2 + 15x + -2x = (7 + -1x)(7 + x) Combine like terms: 3 + 2 = 5 5 + 15x + -2x = (7 + -1x)(7 + x) Combine like terms: 15x + -2x = 13x 5 + 13x = (7 + -1x)(7 + x) Multiply (7 + -1x) * (7 + x) 5 + 13x = (7(7 + x) + -1x * (7 + x)) 5 + 13x = ((7 * 7 + x * 7) + -1x * (7 + x)) 5 + 13x = ((49 + 7x) + -1x * (7 + x)) 5 + 13x = (49 + 7x + (7 * -1x + x * -1x)) 5 + 13x = (49 + 7x + (-7x + -1x2)) Combine like terms: 7x + -7x = 0 5 + 13x = (49 + 0 + -1x2) 5 + 13x = (49 + -1x2) Solving 5 + 13x = 49 + -1x2 Solving for variable 'x'. Reorder the terms: 5 + -49 + 13x + x2 = 49 + -1x2 + -49 + x2 Combine like terms: 5 + -49 = -44 -44 + 13x + x2 = 49 + -1x2 + -49 + x2 Reorder the terms: -44 + 13x + x2 = 49 + -49 + -1x2 + x2 Combine like terms: 49 + -49 = 0 -44 + 13x + x2 = 0 + -1x2 + x2 -44 + 13x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -44 + 13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + 13x + 44 + x2 = 0 + 44 Reorder the terms: -44 + 44 + 13x + x2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + 13x + x2 = 0 + 44 13x + x2 = 0 + 44 Combine like terms: 0 + 44 = 44 13x + x2 = 44 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = 44 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 44 + 42.25 Combine like terms: 44 + 42.25 = 86.25 42.25 + 13x + x2 = 86.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 86.25 Calculate the square root of the right side: 9.287087811 Break this problem into two subproblems by setting (x + 6.5) equal to 9.287087811 and -9.287087811.Subproblem 1
x + 6.5 = 9.287087811 Simplifying x + 6.5 = 9.287087811 Reorder the terms: 6.5 + x = 9.287087811 Solving 6.5 + x = 9.287087811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 9.287087811 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 9.287087811 + -6.5 x = 9.287087811 + -6.5 Combine like terms: 9.287087811 + -6.5 = 2.787087811 x = 2.787087811 Simplifying x = 2.787087811Subproblem 2
x + 6.5 = -9.287087811 Simplifying x + 6.5 = -9.287087811 Reorder the terms: 6.5 + x = -9.287087811 Solving 6.5 + x = -9.287087811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -9.287087811 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -9.287087811 + -6.5 x = -9.287087811 + -6.5 Combine like terms: -9.287087811 + -6.5 = -15.787087811 x = -15.787087811 Simplifying x = -15.787087811Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.787087811, -15.787087811}
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