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Simplifying (x + 7)(x + 2) = 76 Reorder the terms: (7 + x)(x + 2) = 76 Reorder the terms: (7 + x)(2 + x) = 76 Multiply (7 + x) * (2 + x) (7(2 + x) + x(2 + x)) = 76 ((2 * 7 + x * 7) + x(2 + x)) = 76 ((14 + 7x) + x(2 + x)) = 76 (14 + 7x + (2 * x + x * x)) = 76 (14 + 7x + (2x + x2)) = 76 Combine like terms: 7x + 2x = 9x (14 + 9x + x2) = 76 Solving 14 + 9x + x2 = 76 Solving for variable 'x'. Reorder the terms: 14 + -76 + 9x + x2 = 76 + -76 Combine like terms: 14 + -76 = -62 -62 + 9x + x2 = 76 + -76 Combine like terms: 76 + -76 = 0 -62 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '62' to each side of the equation. -62 + 9x + 62 + x2 = 0 + 62 Reorder the terms: -62 + 62 + 9x + x2 = 0 + 62 Combine like terms: -62 + 62 = 0 0 + 9x + x2 = 0 + 62 9x + x2 = 0 + 62 Combine like terms: 0 + 62 = 62 9x + x2 = 62 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 62 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 62 + 20.25 Combine like terms: 62 + 20.25 = 82.25 20.25 + 9x + x2 = 82.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 82.25 Calculate the square root of the right side: 9.069178574 Break this problem into two subproblems by setting (x + 4.5) equal to 9.069178574 and -9.069178574.Subproblem 1
x + 4.5 = 9.069178574 Simplifying x + 4.5 = 9.069178574 Reorder the terms: 4.5 + x = 9.069178574 Solving 4.5 + x = 9.069178574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 9.069178574 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 9.069178574 + -4.5 x = 9.069178574 + -4.5 Combine like terms: 9.069178574 + -4.5 = 4.569178574 x = 4.569178574 Simplifying x = 4.569178574Subproblem 2
x + 4.5 = -9.069178574 Simplifying x + 4.5 = -9.069178574 Reorder the terms: 4.5 + x = -9.069178574 Solving 4.5 + x = -9.069178574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -9.069178574 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -9.069178574 + -4.5 x = -9.069178574 + -4.5 Combine like terms: -9.069178574 + -4.5 = -13.569178574 x = -13.569178574 Simplifying x = -13.569178574Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.569178574, -13.569178574}
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