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Simplifying 99 + -1(7x + 11) = 7(x + 4) * x Reorder the terms: 99 + -1(11 + 7x) = 7(x + 4) * x 99 + (11 * -1 + 7x * -1) = 7(x + 4) * x 99 + (-11 + -7x) = 7(x + 4) * x Combine like terms: 99 + -11 = 88 88 + -7x = 7(x + 4) * x Reorder the terms: 88 + -7x = 7(4 + x) * x Reorder the terms for easier multiplication: 88 + -7x = 7x(4 + x) 88 + -7x = (4 * 7x + x * 7x) 88 + -7x = (28x + 7x2) Solving 88 + -7x = 28x + 7x2 Solving for variable 'x'. Combine like terms: -7x + -28x = -35x 88 + -35x + -7x2 = 28x + 7x2 + -28x + -7x2 Reorder the terms: 88 + -35x + -7x2 = 28x + -28x + 7x2 + -7x2 Combine like terms: 28x + -28x = 0 88 + -35x + -7x2 = 0 + 7x2 + -7x2 88 + -35x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 88 + -35x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -12.57142857 + 5x + x2 = 0 Move the constant term to the right: Add '12.57142857' to each side of the equation. -12.57142857 + 5x + 12.57142857 + x2 = 0 + 12.57142857 Reorder the terms: -12.57142857 + 12.57142857 + 5x + x2 = 0 + 12.57142857 Combine like terms: -12.57142857 + 12.57142857 = 0.00000000 0.00000000 + 5x + x2 = 0 + 12.57142857 5x + x2 = 0 + 12.57142857 Combine like terms: 0 + 12.57142857 = 12.57142857 5x + x2 = 12.57142857 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 12.57142857 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 12.57142857 + 6.25 Combine like terms: 12.57142857 + 6.25 = 18.82142857 6.25 + 5x + x2 = 18.82142857 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 18.82142857 Calculate the square root of the right side: 4.33836704 Break this problem into two subproblems by setting (x + 2.5) equal to 4.33836704 and -4.33836704.Subproblem 1
x + 2.5 = 4.33836704 Simplifying x + 2.5 = 4.33836704 Reorder the terms: 2.5 + x = 4.33836704 Solving 2.5 + x = 4.33836704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 4.33836704 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 4.33836704 + -2.5 x = 4.33836704 + -2.5 Combine like terms: 4.33836704 + -2.5 = 1.83836704 x = 1.83836704 Simplifying x = 1.83836704Subproblem 2
x + 2.5 = -4.33836704 Simplifying x + 2.5 = -4.33836704 Reorder the terms: 2.5 + x = -4.33836704 Solving 2.5 + x = -4.33836704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -4.33836704 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -4.33836704 + -2.5 x = -4.33836704 + -2.5 Combine like terms: -4.33836704 + -2.5 = -6.83836704 x = -6.83836704 Simplifying x = -6.83836704Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.83836704, -6.83836704}
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