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Simplifying (9 + x)(5 + x) = 90 Multiply (9 + x) * (5 + x) (9(5 + x) + x(5 + x)) = 90 ((5 * 9 + x * 9) + x(5 + x)) = 90 ((45 + 9x) + x(5 + x)) = 90 (45 + 9x + (5 * x + x * x)) = 90 (45 + 9x + (5x + x2)) = 90 Combine like terms: 9x + 5x = 14x (45 + 14x + x2) = 90 Solving 45 + 14x + x2 = 90 Solving for variable 'x'. Reorder the terms: 45 + -90 + 14x + x2 = 90 + -90 Combine like terms: 45 + -90 = -45 -45 + 14x + x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -45 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + 14x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 14x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 14x + x2 = 0 + 45 14x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 14x + x2 = 45 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 = 45 + 49 Reorder the terms: 49 + 14x + x2 = 45 + 49 Combine like terms: 45 + 49 = 94 49 + 14x + x2 = 94 Factor a perfect square on the left side: (x + 7)(x + 7) = 94 Calculate the square root of the right side: 9.695359715 Break this problem into two subproblems by setting (x + 7) equal to 9.695359715 and -9.695359715.Subproblem 1
x + 7 = 9.695359715 Simplifying x + 7 = 9.695359715 Reorder the terms: 7 + x = 9.695359715 Solving 7 + x = 9.695359715 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 = 9.695359715 + -7 Combine like terms: 7 + -7 = 0 0 + x = 9.695359715 + -7 x = 9.695359715 + -7 Combine like terms: 9.695359715 + -7 = 2.695359715 x = 2.695359715 Simplifying x = 2.695359715Subproblem 2
x + 7 = -9.695359715 Simplifying x + 7 = -9.695359715 Reorder the terms: 7 + x = -9.695359715 Solving 7 + x = -9.695359715 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 = -9.695359715 + -7 Combine like terms: 7 + -7 = 0 0 + x = -9.695359715 + -7 x = -9.695359715 + -7 Combine like terms: -9.695359715 + -7 = -16.695359715 x = -16.695359715 Simplifying x = -16.695359715Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.695359715, -16.695359715}
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