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Simplifying (x + -3)(x + -10) = 21 Reorder the terms: (-3 + x)(x + -10) = 21 Reorder the terms: (-3 + x)(-10 + x) = 21 Multiply (-3 + x) * (-10 + x) (-3(-10 + x) + x(-10 + x)) = 21 ((-10 * -3 + x * -3) + x(-10 + x)) = 21 ((30 + -3x) + x(-10 + x)) = 21 (30 + -3x + (-10 * x + x * x)) = 21 (30 + -3x + (-10x + x2)) = 21 Combine like terms: -3x + -10x = -13x (30 + -13x + x2) = 21 Solving 30 + -13x + x2 = 21 Solving for variable 'x'. Reorder the terms: 30 + -21 + -13x + x2 = 21 + -21 Combine like terms: 30 + -21 = 9 9 + -13x + x2 = 21 + -21 Combine like terms: 21 + -21 = 0 9 + -13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -13x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -13x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -13x + x2 = 0 + -9 -13x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -13x + x2 = -9 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 = -9 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -9 + 42.25 Combine like terms: -9 + 42.25 = 33.25 42.25 + -13x + x2 = 33.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 33.25 Calculate the square root of the right side: 5.766281297 Break this problem into two subproblems by setting (x + -6.5) equal to 5.766281297 and -5.766281297.Subproblem 1
x + -6.5 = 5.766281297 Simplifying x + -6.5 = 5.766281297 Reorder the terms: -6.5 + x = 5.766281297 Solving -6.5 + x = 5.766281297 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 = 5.766281297 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 5.766281297 + 6.5 x = 5.766281297 + 6.5 Combine like terms: 5.766281297 + 6.5 = 12.266281297 x = 12.266281297 Simplifying x = 12.266281297Subproblem 2
x + -6.5 = -5.766281297 Simplifying x + -6.5 = -5.766281297 Reorder the terms: -6.5 + x = -5.766281297 Solving -6.5 + x = -5.766281297 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 = -5.766281297 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -5.766281297 + 6.5 x = -5.766281297 + 6.5 Combine like terms: -5.766281297 + 6.5 = 0.733718703 x = 0.733718703 Simplifying x = 0.733718703Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.266281297, 0.733718703}
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