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Simplifying x2 + 5x + -154 = 0 Reorder the terms: -154 + 5x + x2 = 0 Solving -154 + 5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '154' to each side of the equation. -154 + 5x + 154 + x2 = 0 + 154 Reorder the terms: -154 + 154 + 5x + x2 = 0 + 154 Combine like terms: -154 + 154 = 0 0 + 5x + x2 = 0 + 154 5x + x2 = 0 + 154 Combine like terms: 0 + 154 = 154 5x + x2 = 154 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 = 154 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 154 + 6.25 Combine like terms: 154 + 6.25 = 160.25 6.25 + 5x + x2 = 160.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 160.25 Calculate the square root of the right side: 12.658988901 Break this problem into two subproblems by setting (x + 2.5) equal to 12.658988901 and -12.658988901.Subproblem 1
x + 2.5 = 12.658988901 Simplifying x + 2.5 = 12.658988901 Reorder the terms: 2.5 + x = 12.658988901 Solving 2.5 + x = 12.658988901 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 = 12.658988901 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 12.658988901 + -2.5 x = 12.658988901 + -2.5 Combine like terms: 12.658988901 + -2.5 = 10.158988901 x = 10.158988901 Simplifying x = 10.158988901Subproblem 2
x + 2.5 = -12.658988901 Simplifying x + 2.5 = -12.658988901 Reorder the terms: 2.5 + x = -12.658988901 Solving 2.5 + x = -12.658988901 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 = -12.658988901 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -12.658988901 + -2.5 x = -12.658988901 + -2.5 Combine like terms: -12.658988901 + -2.5 = -15.158988901 x = -15.158988901 Simplifying x = -15.158988901Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.158988901, -15.158988901}
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