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Simplifying x2 + 29x + -190 = 0 Reorder the terms: -190 + 29x + x2 = 0 Solving -190 + 29x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '190' to each side of the equation. -190 + 29x + 190 + x2 = 0 + 190 Reorder the terms: -190 + 190 + 29x + x2 = 0 + 190 Combine like terms: -190 + 190 = 0 0 + 29x + x2 = 0 + 190 29x + x2 = 0 + 190 Combine like terms: 0 + 190 = 190 29x + x2 = 190 The x term is 29x. Take half its coefficient (14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. 29x + 210.25 + x2 = 190 + 210.25 Reorder the terms: 210.25 + 29x + x2 = 190 + 210.25 Combine like terms: 190 + 210.25 = 400.25 210.25 + 29x + x2 = 400.25 Factor a perfect square on the left side: (x + 14.5)(x + 14.5) = 400.25 Calculate the square root of the right side: 20.006249024 Break this problem into two subproblems by setting (x + 14.5) equal to 20.006249024 and -20.006249024.Subproblem 1
x + 14.5 = 20.006249024 Simplifying x + 14.5 = 20.006249024 Reorder the terms: 14.5 + x = 20.006249024 Solving 14.5 + x = 20.006249024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = 20.006249024 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = 20.006249024 + -14.5 x = 20.006249024 + -14.5 Combine like terms: 20.006249024 + -14.5 = 5.506249024 x = 5.506249024 Simplifying x = 5.506249024Subproblem 2
x + 14.5 = -20.006249024 Simplifying x + 14.5 = -20.006249024 Reorder the terms: 14.5 + x = -20.006249024 Solving 14.5 + x = -20.006249024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = -20.006249024 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = -20.006249024 + -14.5 x = -20.006249024 + -14.5 Combine like terms: -20.006249024 + -14.5 = -34.506249024 x = -34.506249024 Simplifying x = -34.506249024Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.506249024, -34.506249024}
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