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Simplifying x2 + -19x + 35 = 0 Reorder the terms: 35 + -19x + x2 = 0 Solving 35 + -19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + -19x + -35 + x2 = 0 + -35 Reorder the terms: 35 + -35 + -19x + x2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -19x + x2 = 0 + -35 -19x + x2 = 0 + -35 Combine like terms: 0 + -35 = -35 -19x + x2 = -35 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 = -35 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -35 + 90.25 Combine like terms: -35 + 90.25 = 55.25 90.25 + -19x + x2 = 55.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 55.25 Calculate the square root of the right side: 7.433034374 Break this problem into two subproblems by setting (x + -9.5) equal to 7.433034374 and -7.433034374.Subproblem 1
x + -9.5 = 7.433034374 Simplifying x + -9.5 = 7.433034374 Reorder the terms: -9.5 + x = 7.433034374 Solving -9.5 + x = 7.433034374 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 = 7.433034374 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 7.433034374 + 9.5 x = 7.433034374 + 9.5 Combine like terms: 7.433034374 + 9.5 = 16.933034374 x = 16.933034374 Simplifying x = 16.933034374Subproblem 2
x + -9.5 = -7.433034374 Simplifying x + -9.5 = -7.433034374 Reorder the terms: -9.5 + x = -7.433034374 Solving -9.5 + x = -7.433034374 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 = -7.433034374 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -7.433034374 + 9.5 x = -7.433034374 + 9.5 Combine like terms: -7.433034374 + 9.5 = 2.066965626 x = 2.066965626 Simplifying x = 2.066965626Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.933034374, 2.066965626}
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