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Simplifying (x + 7)(x + 9) = 25 Reorder the terms: (7 + x)(x + 9) = 25 Reorder the terms: (7 + x)(9 + x) = 25 Multiply (7 + x) * (9 + x) (7(9 + x) + x(9 + x)) = 25 ((9 * 7 + x * 7) + x(9 + x)) = 25 ((63 + 7x) + x(9 + x)) = 25 (63 + 7x + (9 * x + x * x)) = 25 (63 + 7x + (9x + x2)) = 25 Combine like terms: 7x + 9x = 16x (63 + 16x + x2) = 25 Solving 63 + 16x + x2 = 25 Solving for variable 'x'. Reorder the terms: 63 + -25 + 16x + x2 = 25 + -25 Combine like terms: 63 + -25 = 38 38 + 16x + x2 = 25 + -25 Combine like terms: 25 + -25 = 0 38 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-38' to each side of the equation. 38 + 16x + -38 + x2 = 0 + -38 Reorder the terms: 38 + -38 + 16x + x2 = 0 + -38 Combine like terms: 38 + -38 = 0 0 + 16x + x2 = 0 + -38 16x + x2 = 0 + -38 Combine like terms: 0 + -38 = -38 16x + x2 = -38 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = -38 + 64 Reorder the terms: 64 + 16x + x2 = -38 + 64 Combine like terms: -38 + 64 = 26 64 + 16x + x2 = 26 Factor a perfect square on the left side: (x + 8)(x + 8) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (x + 8) equal to 5.099019514 and -5.099019514.Subproblem 1
x + 8 = 5.099019514 Simplifying x + 8 = 5.099019514 Reorder the terms: 8 + x = 5.099019514 Solving 8 + x = 5.099019514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 5.099019514 + -8 Combine like terms: 8 + -8 = 0 0 + x = 5.099019514 + -8 x = 5.099019514 + -8 Combine like terms: 5.099019514 + -8 = -2.900980486 x = -2.900980486 Simplifying x = -2.900980486Subproblem 2
x + 8 = -5.099019514 Simplifying x + 8 = -5.099019514 Reorder the terms: 8 + x = -5.099019514 Solving 8 + x = -5.099019514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -5.099019514 + -8 Combine like terms: 8 + -8 = 0 0 + x = -5.099019514 + -8 x = -5.099019514 + -8 Combine like terms: -5.099019514 + -8 = -13.099019514 x = -13.099019514 Simplifying x = -13.099019514Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.900980486, -13.099019514}
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