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Simplifying (10 + x)(10 + -1x) = x + -6 Multiply (10 + x) * (10 + -1x) (10(10 + -1x) + x(10 + -1x)) = x + -6 ((10 * 10 + -1x * 10) + x(10 + -1x)) = x + -6 ((100 + -10x) + x(10 + -1x)) = x + -6 (100 + -10x + (10 * x + -1x * x)) = x + -6 (100 + -10x + (10x + -1x2)) = x + -6 Combine like terms: -10x + 10x = 0 (100 + 0 + -1x2) = x + -6 (100 + -1x2) = x + -6 Reorder the terms: 100 + -1x2 = -6 + x Solving 100 + -1x2 = -6 + x Solving for variable 'x'. Reorder the terms: 100 + 6 + -1x + -1x2 = -6 + x + 6 + -1x Combine like terms: 100 + 6 = 106 106 + -1x + -1x2 = -6 + x + 6 + -1x Reorder the terms: 106 + -1x + -1x2 = -6 + 6 + x + -1x Combine like terms: -6 + 6 = 0 106 + -1x + -1x2 = 0 + x + -1x 106 + -1x + -1x2 = x + -1x Combine like terms: x + -1x = 0 106 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -106 + x + x2 = 0 Move the constant term to the right: Add '106' to each side of the equation. -106 + x + 106 + x2 = 0 + 106 Reorder the terms: -106 + 106 + x + x2 = 0 + 106 Combine like terms: -106 + 106 = 0 0 + x + x2 = 0 + 106 x + x2 = 0 + 106 Combine like terms: 0 + 106 = 106 x + x2 = 106 The x term is x. 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. + 0.25 + x2 = 106 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 106 + 0.25 Combine like terms: 106 + 0.25 = 106.25 1.25 + x2 = 106.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 106.25 Calculate the square root of the right side: 10.307764064 Break this problem into two subproblems by setting (x + 0.5) equal to 10.307764064 and -10.307764064.Subproblem 1
x + 0.5 = 10.307764064 Simplifying x + 0.5 = 10.307764064 Reorder the terms: 0.5 + x = 10.307764064 Solving 0.5 + x = 10.307764064 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 = 10.307764064 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 10.307764064 + -0.5 x = 10.307764064 + -0.5 Combine like terms: 10.307764064 + -0.5 = 9.807764064 x = 9.807764064 Simplifying x = 9.807764064Subproblem 2
x + 0.5 = -10.307764064 Simplifying x + 0.5 = -10.307764064 Reorder the terms: 0.5 + x = -10.307764064 Solving 0.5 + x = -10.307764064 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 = -10.307764064 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -10.307764064 + -0.5 x = -10.307764064 + -0.5 Combine like terms: -10.307764064 + -0.5 = -10.807764064 x = -10.807764064 Simplifying x = -10.807764064Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.807764064, -10.807764064}
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