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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 = 11.624143795 x = 11.624143795 Simplifying x = 11.624143795Subproblem 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 = -6.624143795 x = -6.624143795 Simplifying x = -6.624143795Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.624143795, -6.624143795}
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