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Simplifying (x + -4)(x + 3) = 93 Reorder the terms: (-4 + x)(x + 3) = 93 Reorder the terms: (-4 + x)(3 + x) = 93 Multiply (-4 + x) * (3 + x) (-4(3 + x) + x(3 + x)) = 93 ((3 * -4 + x * -4) + x(3 + x)) = 93 ((-12 + -4x) + x(3 + x)) = 93 (-12 + -4x + (3 * x + x * x)) = 93 (-12 + -4x + (3x + x2)) = 93 Combine like terms: -4x + 3x = -1x (-12 + -1x + x2) = 93 Solving -12 + -1x + x2 = 93 Solving for variable 'x'. Reorder the terms: -12 + -93 + -1x + x2 = 93 + -93 Combine like terms: -12 + -93 = -105 -105 + -1x + x2 = 93 + -93 Combine like terms: 93 + -93 = 0 -105 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '105' to each side of the equation. -105 + -1x + 105 + x2 = 0 + 105 Reorder the terms: -105 + 105 + -1x + x2 = 0 + 105 Combine like terms: -105 + 105 = 0 0 + -1x + x2 = 0 + 105 -1x + x2 = 0 + 105 Combine like terms: 0 + 105 = 105 -1x + x2 = 105 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 105 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 105 + 0.25 Combine like terms: 105 + 0.25 = 105.25 0.25 + -1x + x2 = 105.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 105.25 Calculate the square root of the right side: 10.259142264 Break this problem into two subproblems by setting (x + -0.5) equal to 10.259142264 and -10.259142264.Subproblem 1
x + -0.5 = 10.259142264 Simplifying x + -0.5 = 10.259142264 Reorder the terms: -0.5 + x = 10.259142264 Solving -0.5 + x = 10.259142264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 10.259142264 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 10.259142264 + 0.5 x = 10.259142264 + 0.5 Combine like terms: 10.259142264 + 0.5 = 10.759142264 x = 10.759142264 Simplifying x = 10.759142264Subproblem 2
x + -0.5 = -10.259142264 Simplifying x + -0.5 = -10.259142264 Reorder the terms: -0.5 + x = -10.259142264 Solving -0.5 + x = -10.259142264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -10.259142264 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -10.259142264 + 0.5 x = -10.259142264 + 0.5 Combine like terms: -10.259142264 + 0.5 = -9.759142264 x = -9.759142264 Simplifying x = -9.759142264Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.759142264, -9.759142264}
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