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Simplifying 92 = (7 + x)(12 + x) Multiply (7 + x) * (12 + x) 92 = (7(12 + x) + x(12 + x)) 92 = ((12 * 7 + x * 7) + x(12 + x)) 92 = ((84 + 7x) + x(12 + x)) 92 = (84 + 7x + (12 * x + x * x)) 92 = (84 + 7x + (12x + x2)) Combine like terms: 7x + 12x = 19x 92 = (84 + 19x + x2) Solving 92 = 84 + 19x + x2 Solving for variable 'x'. Combine like terms: 92 + -84 = 8 8 + -19x + -1x2 = 84 + 19x + x2 + -84 + -19x + -1x2 Reorder the terms: 8 + -19x + -1x2 = 84 + -84 + 19x + -19x + x2 + -1x2 Combine like terms: 84 + -84 = 0 8 + -19x + -1x2 = 0 + 19x + -19x + x2 + -1x2 8 + -19x + -1x2 = 19x + -19x + x2 + -1x2 Combine like terms: 19x + -19x = 0 8 + -19x + -1x2 = 0 + x2 + -1x2 8 + -19x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 8 + -19x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + 19x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 19x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 19x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 19x + x2 = 0 + 8 19x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 19x + x2 = 8 The x term is 19x. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19x + 90.25 + x2 = 8 + 90.25 Reorder the terms: 90.25 + 19x + x2 = 8 + 90.25 Combine like terms: 8 + 90.25 = 98.25 90.25 + 19x + x2 = 98.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 98.25 Calculate the square root of the right side: 9.912113801 Break this problem into two subproblems by setting (x + 9.5) equal to 9.912113801 and -9.912113801.Subproblem 1
x + 9.5 = 9.912113801 Simplifying x + 9.5 = 9.912113801 Reorder the terms: 9.5 + x = 9.912113801 Solving 9.5 + x = 9.912113801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 9.912113801 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 9.912113801 + -9.5 x = 9.912113801 + -9.5 Combine like terms: 9.912113801 + -9.5 = 0.412113801 x = 0.412113801 Simplifying x = 0.412113801Subproblem 2
x + 9.5 = -9.912113801 Simplifying x + 9.5 = -9.912113801 Reorder the terms: 9.5 + x = -9.912113801 Solving 9.5 + x = -9.912113801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -9.912113801 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -9.912113801 + -9.5 x = -9.912113801 + -9.5 Combine like terms: -9.912113801 + -9.5 = -19.412113801 x = -19.412113801 Simplifying x = -19.412113801Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.412113801, -19.412113801}
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