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Simplifying x2 + -17x + -28 = 0 Reorder the terms: -28 + -17x + x2 = 0 Solving -28 + -17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + -17x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + -17x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -17x + x2 = 0 + 28 -17x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 -17x + x2 = 28 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 = 28 + 72.25 Reorder the terms: 72.25 + -17x + x2 = 28 + 72.25 Combine like terms: 28 + 72.25 = 100.25 72.25 + -17x + x2 = 100.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 100.25 Calculate the square root of the right side: 10.012492197 Break this problem into two subproblems by setting (x + -8.5) equal to 10.012492197 and -10.012492197.Subproblem 1
x + -8.5 = 10.012492197 Simplifying x + -8.5 = 10.012492197 Reorder the terms: -8.5 + x = 10.012492197 Solving -8.5 + x = 10.012492197 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 = 10.012492197 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 10.012492197 + 8.5 x = 10.012492197 + 8.5 Combine like terms: 10.012492197 + 8.5 = 18.512492197 x = 18.512492197 Simplifying x = 18.512492197Subproblem 2
x + -8.5 = -10.012492197 Simplifying x + -8.5 = -10.012492197 Reorder the terms: -8.5 + x = -10.012492197 Solving -8.5 + x = -10.012492197 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 = -10.012492197 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -10.012492197 + 8.5 x = -10.012492197 + 8.5 Combine like terms: -10.012492197 + 8.5 = -1.512492197 x = -1.512492197 Simplifying x = -1.512492197Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.512492197, -1.512492197}
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