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Simplifying x2 + 5x + -69 = 0 Reorder the terms: -69 + 5x + x2 = 0 Solving -69 + 5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '69' to each side of the equation. -69 + 5x + 69 + x2 = 0 + 69 Reorder the terms: -69 + 69 + 5x + x2 = 0 + 69 Combine like terms: -69 + 69 = 0 0 + 5x + x2 = 0 + 69 5x + x2 = 0 + 69 Combine like terms: 0 + 69 = 69 5x + x2 = 69 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 = 69 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 69 + 6.25 Combine like terms: 69 + 6.25 = 75.25 6.25 + 5x + x2 = 75.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 75.25 Calculate the square root of the right side: 8.674675786 Break this problem into two subproblems by setting (x + 2.5) equal to 8.674675786 and -8.674675786.Subproblem 1
x + 2.5 = 8.674675786 Simplifying x + 2.5 = 8.674675786 Reorder the terms: 2.5 + x = 8.674675786 Solving 2.5 + x = 8.674675786 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 = 8.674675786 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 8.674675786 + -2.5 x = 8.674675786 + -2.5 Combine like terms: 8.674675786 + -2.5 = 6.174675786 x = 6.174675786 Simplifying x = 6.174675786Subproblem 2
x + 2.5 = -8.674675786 Simplifying x + 2.5 = -8.674675786 Reorder the terms: 2.5 + x = -8.674675786 Solving 2.5 + x = -8.674675786 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 = -8.674675786 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -8.674675786 + -2.5 x = -8.674675786 + -2.5 Combine like terms: -8.674675786 + -2.5 = -11.174675786 x = -11.174675786 Simplifying x = -11.174675786Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.174675786, -11.174675786}
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