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Simplifying (x + 9)(x + 5) = 170 Reorder the terms: (9 + x)(x + 5) = 170 Reorder the terms: (9 + x)(5 + x) = 170 Multiply (9 + x) * (5 + x) (9(5 + x) + x(5 + x)) = 170 ((5 * 9 + x * 9) + x(5 + x)) = 170 ((45 + 9x) + x(5 + x)) = 170 (45 + 9x + (5 * x + x * x)) = 170 (45 + 9x + (5x + x2)) = 170 Combine like terms: 9x + 5x = 14x (45 + 14x + x2) = 170 Solving 45 + 14x + x2 = 170 Solving for variable 'x'. Reorder the terms: 45 + -170 + 14x + x2 = 170 + -170 Combine like terms: 45 + -170 = -125 -125 + 14x + x2 = 170 + -170 Combine like terms: 170 + -170 = 0 -125 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '125' to each side of the equation. -125 + 14x + 125 + x2 = 0 + 125 Reorder the terms: -125 + 125 + 14x + x2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + 14x + x2 = 0 + 125 14x + x2 = 0 + 125 Combine like terms: 0 + 125 = 125 14x + x2 = 125 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 = 125 + 49 Reorder the terms: 49 + 14x + x2 = 125 + 49 Combine like terms: 125 + 49 = 174 49 + 14x + x2 = 174 Factor a perfect square on the left side: (x + 7)(x + 7) = 174 Calculate the square root of the right side: 13.190905958 Break this problem into two subproblems by setting (x + 7) equal to 13.190905958 and -13.190905958.Subproblem 1
x + 7 = 13.190905958 Simplifying x + 7 = 13.190905958 Reorder the terms: 7 + x = 13.190905958 Solving 7 + x = 13.190905958 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 = 13.190905958 + -7 Combine like terms: 7 + -7 = 0 0 + x = 13.190905958 + -7 x = 13.190905958 + -7 Combine like terms: 13.190905958 + -7 = 6.190905958 x = 6.190905958 Simplifying x = 6.190905958Subproblem 2
x + 7 = -13.190905958 Simplifying x + 7 = -13.190905958 Reorder the terms: 7 + x = -13.190905958 Solving 7 + x = -13.190905958 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 = -13.190905958 + -7 Combine like terms: 7 + -7 = 0 0 + x = -13.190905958 + -7 x = -13.190905958 + -7 Combine like terms: -13.190905958 + -7 = -20.190905958 x = -20.190905958 Simplifying x = -20.190905958Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.190905958, -20.190905958}
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