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Simplifying 100 = (x + 11)(x + -5) Reorder the terms: 100 = (11 + x)(x + -5) Reorder the terms: 100 = (11 + x)(-5 + x) Multiply (11 + x) * (-5 + x) 100 = (11(-5 + x) + x(-5 + x)) 100 = ((-5 * 11 + x * 11) + x(-5 + x)) 100 = ((-55 + 11x) + x(-5 + x)) 100 = (-55 + 11x + (-5 * x + x * x)) 100 = (-55 + 11x + (-5x + x2)) Combine like terms: 11x + -5x = 6x 100 = (-55 + 6x + x2) Solving 100 = -55 + 6x + x2 Solving for variable 'x'. Combine like terms: 100 + 55 = 155 155 + -6x + -1x2 = -55 + 6x + x2 + 55 + -6x + -1x2 Reorder the terms: 155 + -6x + -1x2 = -55 + 55 + 6x + -6x + x2 + -1x2 Combine like terms: -55 + 55 = 0 155 + -6x + -1x2 = 0 + 6x + -6x + x2 + -1x2 155 + -6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 155 + -6x + -1x2 = 0 + x2 + -1x2 155 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 155 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -155 + 6x + x2 = 0 Move the constant term to the right: Add '155' to each side of the equation. -155 + 6x + 155 + x2 = 0 + 155 Reorder the terms: -155 + 155 + 6x + x2 = 0 + 155 Combine like terms: -155 + 155 = 0 0 + 6x + x2 = 0 + 155 6x + x2 = 0 + 155 Combine like terms: 0 + 155 = 155 6x + x2 = 155 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 155 + 9 Reorder the terms: 9 + 6x + x2 = 155 + 9 Combine like terms: 155 + 9 = 164 9 + 6x + x2 = 164 Factor a perfect square on the left side: (x + 3)(x + 3) = 164 Calculate the square root of the right side: 12.806248475 Break this problem into two subproblems by setting (x + 3) equal to 12.806248475 and -12.806248475.Subproblem 1
x + 3 = 12.806248475 Simplifying x + 3 = 12.806248475 Reorder the terms: 3 + x = 12.806248475 Solving 3 + x = 12.806248475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 12.806248475 + -3 Combine like terms: 3 + -3 = 0 0 + x = 12.806248475 + -3 x = 12.806248475 + -3 Combine like terms: 12.806248475 + -3 = 9.806248475 x = 9.806248475 Simplifying x = 9.806248475Subproblem 2
x + 3 = -12.806248475 Simplifying x + 3 = -12.806248475 Reorder the terms: 3 + x = -12.806248475 Solving 3 + x = -12.806248475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -12.806248475 + -3 Combine like terms: 3 + -3 = 0 0 + x = -12.806248475 + -3 x = -12.806248475 + -3 Combine like terms: -12.806248475 + -3 = -15.806248475 x = -15.806248475 Simplifying x = -15.806248475Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.806248475, -15.806248475}
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