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Simplifying x2 + -17x + 40 = 0 Reorder the terms: 40 + -17x + x2 = 0 Solving 40 + -17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + -17x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + -17x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -17x + x2 = 0 + -40 -17x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 -17x + x2 = -40 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = -40 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -40 + 72.25 Combine like terms: -40 + 72.25 = 32.25 72.25 + -17x + x2 = 32.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (x + -8.5) equal to 5.678908346 and -5.678908346.Subproblem 1
x + -8.5 = 5.678908346 Simplifying x + -8.5 = 5.678908346 Reorder the terms: -8.5 + x = 5.678908346 Solving -8.5 + x = 5.678908346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 5.678908346 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 5.678908346 + 8.5 x = 5.678908346 + 8.5 Combine like terms: 5.678908346 + 8.5 = 14.178908346 x = 14.178908346 Simplifying x = 14.178908346Subproblem 2
x + -8.5 = -5.678908346 Simplifying x + -8.5 = -5.678908346 Reorder the terms: -8.5 + x = -5.678908346 Solving -8.5 + x = -5.678908346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -5.678908346 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -5.678908346 + 8.5 x = -5.678908346 + 8.5 Combine like terms: -5.678908346 + 8.5 = 2.821091654 x = 2.821091654 Simplifying x = 2.821091654Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.178908346, 2.821091654}
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