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Simplifying (x + 9)(x + -10) = 6 Reorder the terms: (9 + x)(x + -10) = 6 Reorder the terms: (9 + x)(-10 + x) = 6 Multiply (9 + x) * (-10 + x) (9(-10 + x) + x(-10 + x)) = 6 ((-10 * 9 + x * 9) + x(-10 + x)) = 6 ((-90 + 9x) + x(-10 + x)) = 6 (-90 + 9x + (-10 * x + x * x)) = 6 (-90 + 9x + (-10x + x2)) = 6 Combine like terms: 9x + -10x = -1x (-90 + -1x + x2) = 6 Solving -90 + -1x + x2 = 6 Solving for variable 'x'. Reorder the terms: -90 + -6 + -1x + x2 = 6 + -6 Combine like terms: -90 + -6 = -96 -96 + -1x + x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -96 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '96' to each side of the equation. -96 + -1x + 96 + x2 = 0 + 96 Reorder the terms: -96 + 96 + -1x + x2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + -1x + x2 = 0 + 96 -1x + x2 = 0 + 96 Combine like terms: 0 + 96 = 96 -1x + x2 = 96 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 = 96 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 96 + 0.25 Combine like terms: 96 + 0.25 = 96.25 0.25 + -1x + x2 = 96.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 96.25 Calculate the square root of the right side: 9.810708435 Break this problem into two subproblems by setting (x + -0.5) equal to 9.810708435 and -9.810708435.Subproblem 1
x + -0.5 = 9.810708435 Simplifying x + -0.5 = 9.810708435 Reorder the terms: -0.5 + x = 9.810708435 Solving -0.5 + x = 9.810708435 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 = 9.810708435 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 9.810708435 + 0.5 x = 9.810708435 + 0.5 Combine like terms: 9.810708435 + 0.5 = 10.310708435 x = 10.310708435 Simplifying x = 10.310708435Subproblem 2
x + -0.5 = -9.810708435 Simplifying x + -0.5 = -9.810708435 Reorder the terms: -0.5 + x = -9.810708435 Solving -0.5 + x = -9.810708435 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 = -9.810708435 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -9.810708435 + 0.5 x = -9.810708435 + 0.5 Combine like terms: -9.810708435 + 0.5 = -9.310708435 x = -9.310708435 Simplifying x = -9.310708435Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.310708435, -9.310708435}
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