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Simplifying (x + 3)(x + -4) = 99 Reorder the terms: (3 + x)(x + -4) = 99 Reorder the terms: (3 + x)(-4 + x) = 99 Multiply (3 + x) * (-4 + x) (3(-4 + x) + x(-4 + x)) = 99 ((-4 * 3 + x * 3) + x(-4 + x)) = 99 ((-12 + 3x) + x(-4 + x)) = 99 (-12 + 3x + (-4 * x + x * x)) = 99 (-12 + 3x + (-4x + x2)) = 99 Combine like terms: 3x + -4x = -1x (-12 + -1x + x2) = 99 Solving -12 + -1x + x2 = 99 Solving for variable 'x'. Reorder the terms: -12 + -99 + -1x + x2 = 99 + -99 Combine like terms: -12 + -99 = -111 -111 + -1x + x2 = 99 + -99 Combine like terms: 99 + -99 = 0 -111 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '111' to each side of the equation. -111 + -1x + 111 + x2 = 0 + 111 Reorder the terms: -111 + 111 + -1x + x2 = 0 + 111 Combine like terms: -111 + 111 = 0 0 + -1x + x2 = 0 + 111 -1x + x2 = 0 + 111 Combine like terms: 0 + 111 = 111 -1x + x2 = 111 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 = 111 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 111 + 0.25 Combine like terms: 111 + 0.25 = 111.25 0.25 + -1x + x2 = 111.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 111.25 Calculate the square root of the right side: 10.547511555 Break this problem into two subproblems by setting (x + -0.5) equal to 10.547511555 and -10.547511555.Subproblem 1
x + -0.5 = 10.547511555 Simplifying x + -0.5 = 10.547511555 Reorder the terms: -0.5 + x = 10.547511555 Solving -0.5 + x = 10.547511555 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 = 10.547511555 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 10.547511555 + 0.5 x = 10.547511555 + 0.5 Combine like terms: 10.547511555 + 0.5 = 11.047511555 x = 11.047511555 Simplifying x = 11.047511555Subproblem 2
x + -0.5 = -10.547511555 Simplifying x + -0.5 = -10.547511555 Reorder the terms: -0.5 + x = -10.547511555 Solving -0.5 + x = -10.547511555 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 = -10.547511555 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -10.547511555 + 0.5 x = -10.547511555 + 0.5 Combine like terms: -10.547511555 + 0.5 = -10.047511555 x = -10.047511555 Simplifying x = -10.047511555Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.047511555, -10.047511555}
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