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Simplifying (x + -4) + (x + 3)(x + -7) = 59 Reorder the terms: (-4 + x) + (x + 3)(x + -7) = 59 Remove parenthesis around (-4 + x) -4 + x + (x + 3)(x + -7) = 59 Reorder the terms: -4 + x + (3 + x)(x + -7) = 59 Reorder the terms: -4 + x + (3 + x)(-7 + x) = 59 Multiply (3 + x) * (-7 + x) -4 + x + (3(-7 + x) + x(-7 + x)) = 59 -4 + x + ((-7 * 3 + x * 3) + x(-7 + x)) = 59 -4 + x + ((-21 + 3x) + x(-7 + x)) = 59 -4 + x + (-21 + 3x + (-7 * x + x * x)) = 59 -4 + x + (-21 + 3x + (-7x + x2)) = 59 Combine like terms: 3x + -7x = -4x -4 + x + (-21 + -4x + x2) = 59 Reorder the terms: -4 + -21 + x + -4x + x2 = 59 Combine like terms: -4 + -21 = -25 -25 + x + -4x + x2 = 59 Combine like terms: x + -4x = -3x -25 + -3x + x2 = 59 Solving -25 + -3x + x2 = 59 Solving for variable 'x'. Reorder the terms: -25 + -59 + -3x + x2 = 59 + -59 Combine like terms: -25 + -59 = -84 -84 + -3x + x2 = 59 + -59 Combine like terms: 59 + -59 = 0 -84 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '84' to each side of the equation. -84 + -3x + 84 + x2 = 0 + 84 Reorder the terms: -84 + 84 + -3x + x2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + -3x + x2 = 0 + 84 -3x + x2 = 0 + 84 Combine like terms: 0 + 84 = 84 -3x + x2 = 84 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 84 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 84 + 2.25 Combine like terms: 84 + 2.25 = 86.25 2.25 + -3x + x2 = 86.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 86.25 Calculate the square root of the right side: 9.287087811 Break this problem into two subproblems by setting (x + -1.5) equal to 9.287087811 and -9.287087811.Subproblem 1
x + -1.5 = 9.287087811 Simplifying x + -1.5 = 9.287087811 Reorder the terms: -1.5 + x = 9.287087811 Solving -1.5 + x = 9.287087811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 9.287087811 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 9.287087811 + 1.5 x = 9.287087811 + 1.5 Combine like terms: 9.287087811 + 1.5 = 10.787087811 x = 10.787087811 Simplifying x = 10.787087811Subproblem 2
x + -1.5 = -9.287087811 Simplifying x + -1.5 = -9.287087811 Reorder the terms: -1.5 + x = -9.287087811 Solving -1.5 + x = -9.287087811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -9.287087811 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -9.287087811 + 1.5 x = -9.287087811 + 1.5 Combine like terms: -9.287087811 + 1.5 = -7.787087811 x = -7.787087811 Simplifying x = -7.787087811Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.787087811, -7.787087811}
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