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Simplifying (x + -3)(x + -5) = 74 Reorder the terms: (-3 + x)(x + -5) = 74 Reorder the terms: (-3 + x)(-5 + x) = 74 Multiply (-3 + x) * (-5 + x) (-3(-5 + x) + x(-5 + x)) = 74 ((-5 * -3 + x * -3) + x(-5 + x)) = 74 ((15 + -3x) + x(-5 + x)) = 74 (15 + -3x + (-5 * x + x * x)) = 74 (15 + -3x + (-5x + x2)) = 74 Combine like terms: -3x + -5x = -8x (15 + -8x + x2) = 74 Solving 15 + -8x + x2 = 74 Solving for variable 'x'. Reorder the terms: 15 + -74 + -8x + x2 = 74 + -74 Combine like terms: 15 + -74 = -59 -59 + -8x + x2 = 74 + -74 Combine like terms: 74 + -74 = 0 -59 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '59' to each side of the equation. -59 + -8x + 59 + x2 = 0 + 59 Reorder the terms: -59 + 59 + -8x + x2 = 0 + 59 Combine like terms: -59 + 59 = 0 0 + -8x + x2 = 0 + 59 -8x + x2 = 0 + 59 Combine like terms: 0 + 59 = 59 -8x + x2 = 59 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 59 + 16 Reorder the terms: 16 + -8x + x2 = 59 + 16 Combine like terms: 59 + 16 = 75 16 + -8x + x2 = 75 Factor a perfect square on the left side: (x + -4)(x + -4) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (x + -4) equal to 8.660254038 and -8.660254038.Subproblem 1
x + -4 = 8.660254038 Simplifying x + -4 = 8.660254038 Reorder the terms: -4 + x = 8.660254038 Solving -4 + x = 8.660254038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 8.660254038 + 4 Combine like terms: -4 + 4 = 0 0 + x = 8.660254038 + 4 x = 8.660254038 + 4 Combine like terms: 8.660254038 + 4 = 12.660254038 x = 12.660254038 Simplifying x = 12.660254038Subproblem 2
x + -4 = -8.660254038 Simplifying x + -4 = -8.660254038 Reorder the terms: -4 + x = -8.660254038 Solving -4 + x = -8.660254038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -8.660254038 + 4 Combine like terms: -4 + 4 = 0 0 + x = -8.660254038 + 4 x = -8.660254038 + 4 Combine like terms: -8.660254038 + 4 = -4.660254038 x = -4.660254038 Simplifying x = -4.660254038Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.660254038, -4.660254038}
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