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Simplifying (x + 7)(x + 9) = 2x + 62 Reorder the terms: (7 + x)(x + 9) = 2x + 62 Reorder the terms: (7 + x)(9 + x) = 2x + 62 Multiply (7 + x) * (9 + x) (7(9 + x) + x(9 + x)) = 2x + 62 ((9 * 7 + x * 7) + x(9 + x)) = 2x + 62 ((63 + 7x) + x(9 + x)) = 2x + 62 (63 + 7x + (9 * x + x * x)) = 2x + 62 (63 + 7x + (9x + x2)) = 2x + 62 Combine like terms: 7x + 9x = 16x (63 + 16x + x2) = 2x + 62 Reorder the terms: 63 + 16x + x2 = 62 + 2x Solving 63 + 16x + x2 = 62 + 2x Solving for variable 'x'. Reorder the terms: 63 + -62 + 16x + -2x + x2 = 62 + 2x + -62 + -2x Combine like terms: 63 + -62 = 1 1 + 16x + -2x + x2 = 62 + 2x + -62 + -2x Combine like terms: 16x + -2x = 14x 1 + 14x + x2 = 62 + 2x + -62 + -2x Reorder the terms: 1 + 14x + x2 = 62 + -62 + 2x + -2x Combine like terms: 62 + -62 = 0 1 + 14x + x2 = 0 + 2x + -2x 1 + 14x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 1 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 14x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 14x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 14x + x2 = 0 + -1 14x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 14x + x2 = -1 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = -1 + 49 Reorder the terms: 49 + 14x + x2 = -1 + 49 Combine like terms: -1 + 49 = 48 49 + 14x + x2 = 48 Factor a perfect square on the left side: (x + 7)(x + 7) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (x + 7) equal to 6.92820323 and -6.92820323.Subproblem 1
x + 7 = 6.92820323 Simplifying x + 7 = 6.92820323 Reorder the terms: 7 + x = 6.92820323 Solving 7 + x = 6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 6.92820323 + -7 Combine like terms: 7 + -7 = 0 0 + x = 6.92820323 + -7 x = 6.92820323 + -7 Combine like terms: 6.92820323 + -7 = -0.07179677 x = -0.07179677 Simplifying x = -0.07179677Subproblem 2
x + 7 = -6.92820323 Simplifying x + 7 = -6.92820323 Reorder the terms: 7 + x = -6.92820323 Solving 7 + x = -6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -6.92820323 + -7 Combine like terms: 7 + -7 = 0 0 + x = -6.92820323 + -7 x = -6.92820323 + -7 Combine like terms: -6.92820323 + -7 = -13.92820323 x = -13.92820323 Simplifying x = -13.92820323Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.07179677, -13.92820323}
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