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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 = -2.066965626 x = -2.066965626 Simplifying x = -2.066965626Subproblem 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 = -16.933034374 x = -16.933034374 Simplifying x = -16.933034374Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.066965626, -16.933034374}
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