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Simplifying -1x2 + 39x + 20 = 0 Reorder the terms: 20 + 39x + -1x2 = 0 Solving 20 + 39x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -20 + -39x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -39x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -39x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -39x + x2 = 0 + 20 -39x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -39x + x2 = 20 The x term is -39x. Take half its coefficient (-19.5). Square it (380.25) and add it to both sides. Add '380.25' to each side of the equation. -39x + 380.25 + x2 = 20 + 380.25 Reorder the terms: 380.25 + -39x + x2 = 20 + 380.25 Combine like terms: 20 + 380.25 = 400.25 380.25 + -39x + x2 = 400.25 Factor a perfect square on the left side: (x + -19.5)(x + -19.5) = 400.25 Calculate the square root of the right side: 20.006249024 Break this problem into two subproblems by setting (x + -19.5) equal to 20.006249024 and -20.006249024.Subproblem 1
x + -19.5 = 20.006249024 Simplifying x + -19.5 = 20.006249024 Reorder the terms: -19.5 + x = 20.006249024 Solving -19.5 + x = 20.006249024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.5' to each side of the equation. -19.5 + 19.5 + x = 20.006249024 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + x = 20.006249024 + 19.5 x = 20.006249024 + 19.5 Combine like terms: 20.006249024 + 19.5 = 39.506249024 x = 39.506249024 Simplifying x = 39.506249024Subproblem 2
x + -19.5 = -20.006249024 Simplifying x + -19.5 = -20.006249024 Reorder the terms: -19.5 + x = -20.006249024 Solving -19.5 + x = -20.006249024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.5' to each side of the equation. -19.5 + 19.5 + x = -20.006249024 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + x = -20.006249024 + 19.5 x = -20.006249024 + 19.5 Combine like terms: -20.006249024 + 19.5 = -0.506249024 x = -0.506249024 Simplifying x = -0.506249024Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.506249024, -0.506249024}
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