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Simplifying x2 + 35x + 19 = 0 Reorder the terms: 19 + 35x + x2 = 0 Solving 19 + 35x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + 35x + -19 + x2 = 0 + -19 Reorder the terms: 19 + -19 + 35x + x2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 35x + x2 = 0 + -19 35x + x2 = 0 + -19 Combine like terms: 0 + -19 = -19 35x + x2 = -19 The x term is 35x. Take half its coefficient (17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. 35x + 306.25 + x2 = -19 + 306.25 Reorder the terms: 306.25 + 35x + x2 = -19 + 306.25 Combine like terms: -19 + 306.25 = 287.25 306.25 + 35x + x2 = 287.25 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = 287.25 Calculate the square root of the right side: 16.948451257 Break this problem into two subproblems by setting (x + 17.5) equal to 16.948451257 and -16.948451257.Subproblem 1
x + 17.5 = 16.948451257 Simplifying x + 17.5 = 16.948451257 Reorder the terms: 17.5 + x = 16.948451257 Solving 17.5 + x = 16.948451257 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = 16.948451257 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 16.948451257 + -17.5 x = 16.948451257 + -17.5 Combine like terms: 16.948451257 + -17.5 = -0.551548743 x = -0.551548743 Simplifying x = -0.551548743Subproblem 2
x + 17.5 = -16.948451257 Simplifying x + 17.5 = -16.948451257 Reorder the terms: 17.5 + x = -16.948451257 Solving 17.5 + x = -16.948451257 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = -16.948451257 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -16.948451257 + -17.5 x = -16.948451257 + -17.5 Combine like terms: -16.948451257 + -17.5 = -34.448451257 x = -34.448451257 Simplifying x = -34.448451257Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.551548743, -34.448451257}
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