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Simplifying x(x + 5) = 77 Reorder the terms: x(5 + x) = 77 (5 * x + x * x) = 77 (5x + x2) = 77 Solving 5x + x2 = 77 Solving for variable 'x'. Reorder the terms: -77 + 5x + x2 = 77 + -77 Combine like terms: 77 + -77 = 0 -77 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '77' to each side of the equation. -77 + 5x + 77 + x2 = 0 + 77 Reorder the terms: -77 + 77 + 5x + x2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + 5x + x2 = 0 + 77 5x + x2 = 0 + 77 Combine like terms: 0 + 77 = 77 5x + x2 = 77 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 77 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 77 + 6.25 Combine like terms: 77 + 6.25 = 83.25 6.25 + 5x + x2 = 83.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 83.25 Calculate the square root of the right side: 9.124143795 Break this problem into two subproblems by setting (x + 2.5) equal to 9.124143795 and -9.124143795.Subproblem 1
x + 2.5 = 9.124143795 Simplifying x + 2.5 = 9.124143795 Reorder the terms: 2.5 + x = 9.124143795 Solving 2.5 + x = 9.124143795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 9.124143795 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 9.124143795 + -2.5 x = 9.124143795 + -2.5 Combine like terms: 9.124143795 + -2.5 = 6.624143795 x = 6.624143795 Simplifying x = 6.624143795Subproblem 2
x + 2.5 = -9.124143795 Simplifying x + 2.5 = -9.124143795 Reorder the terms: 2.5 + x = -9.124143795 Solving 2.5 + x = -9.124143795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -9.124143795 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -9.124143795 + -2.5 x = -9.124143795 + -2.5 Combine like terms: -9.124143795 + -2.5 = -11.624143795 x = -11.624143795 Simplifying x = -11.624143795Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.624143795, -11.624143795}
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