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Simplifying (2x + 19)(x + 7) = 86 Reorder the terms: (19 + 2x)(x + 7) = 86 Reorder the terms: (19 + 2x)(7 + x) = 86 Multiply (19 + 2x) * (7 + x) (19(7 + x) + 2x * (7 + x)) = 86 ((7 * 19 + x * 19) + 2x * (7 + x)) = 86 ((133 + 19x) + 2x * (7 + x)) = 86 (133 + 19x + (7 * 2x + x * 2x)) = 86 (133 + 19x + (14x + 2x2)) = 86 Combine like terms: 19x + 14x = 33x (133 + 33x + 2x2) = 86 Solving 133 + 33x + 2x2 = 86 Solving for variable 'x'. Reorder the terms: 133 + -86 + 33x + 2x2 = 86 + -86 Combine like terms: 133 + -86 = 47 47 + 33x + 2x2 = 86 + -86 Combine like terms: 86 + -86 = 0 47 + 33x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 23.5 + 16.5x + x2 = 0 Move the constant term to the right: Add '-23.5' to each side of the equation. 23.5 + 16.5x + -23.5 + x2 = 0 + -23.5 Reorder the terms: 23.5 + -23.5 + 16.5x + x2 = 0 + -23.5 Combine like terms: 23.5 + -23.5 = 0.0 0.0 + 16.5x + x2 = 0 + -23.5 16.5x + x2 = 0 + -23.5 Combine like terms: 0 + -23.5 = -23.5 16.5x + x2 = -23.5 The x term is 16.5x. Take half its coefficient (8.25). Square it (68.0625) and add it to both sides. Add '68.0625' to each side of the equation. 16.5x + 68.0625 + x2 = -23.5 + 68.0625 Reorder the terms: 68.0625 + 16.5x + x2 = -23.5 + 68.0625 Combine like terms: -23.5 + 68.0625 = 44.5625 68.0625 + 16.5x + x2 = 44.5625 Factor a perfect square on the left side: (x + 8.25)(x + 8.25) = 44.5625 Calculate the square root of the right side: 6.675514961 Break this problem into two subproblems by setting (x + 8.25) equal to 6.675514961 and -6.675514961.Subproblem 1
x + 8.25 = 6.675514961 Simplifying x + 8.25 = 6.675514961 Reorder the terms: 8.25 + x = 6.675514961 Solving 8.25 + x = 6.675514961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.25' to each side of the equation. 8.25 + -8.25 + x = 6.675514961 + -8.25 Combine like terms: 8.25 + -8.25 = 0.00 0.00 + x = 6.675514961 + -8.25 x = 6.675514961 + -8.25 Combine like terms: 6.675514961 + -8.25 = -1.574485039 x = -1.574485039 Simplifying x = -1.574485039Subproblem 2
x + 8.25 = -6.675514961 Simplifying x + 8.25 = -6.675514961 Reorder the terms: 8.25 + x = -6.675514961 Solving 8.25 + x = -6.675514961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.25' to each side of the equation. 8.25 + -8.25 + x = -6.675514961 + -8.25 Combine like terms: 8.25 + -8.25 = 0.00 0.00 + x = -6.675514961 + -8.25 x = -6.675514961 + -8.25 Combine like terms: -6.675514961 + -8.25 = -14.925514961 x = -14.925514961 Simplifying x = -14.925514961Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.574485039, -14.925514961}
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