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Simplifying x2 + -19x + 17 = 0 Reorder the terms: 17 + -19x + x2 = 0 Solving 17 + -19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + -19x + -17 + x2 = 0 + -17 Reorder the terms: 17 + -17 + -19x + x2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -19x + x2 = 0 + -17 -19x + x2 = 0 + -17 Combine like terms: 0 + -17 = -17 -19x + x2 = -17 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = -17 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -17 + 90.25 Combine like terms: -17 + 90.25 = 73.25 90.25 + -19x + x2 = 73.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 73.25 Calculate the square root of the right side: 8.558621384 Break this problem into two subproblems by setting (x + -9.5) equal to 8.558621384 and -8.558621384.Subproblem 1
x + -9.5 = 8.558621384 Simplifying x + -9.5 = 8.558621384 Reorder the terms: -9.5 + x = 8.558621384 Solving -9.5 + x = 8.558621384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 8.558621384 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 8.558621384 + 9.5 x = 8.558621384 + 9.5 Combine like terms: 8.558621384 + 9.5 = 18.058621384 x = 18.058621384 Simplifying x = 18.058621384Subproblem 2
x + -9.5 = -8.558621384 Simplifying x + -9.5 = -8.558621384 Reorder the terms: -9.5 + x = -8.558621384 Solving -9.5 + x = -8.558621384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -8.558621384 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -8.558621384 + 9.5 x = -8.558621384 + 9.5 Combine like terms: -8.558621384 + 9.5 = 0.941378616 x = 0.941378616 Simplifying x = 0.941378616Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.058621384, 0.941378616}
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