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Simplifying 20x2 + -11x + -21 = 0 Reorder the terms: -21 + -11x + 20x2 = 0 Solving -21 + -11x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -1.05 + -0.55x + x2 = 0 Move the constant term to the right: Add '1.05' to each side of the equation. -1.05 + -0.55x + 1.05 + x2 = 0 + 1.05 Reorder the terms: -1.05 + 1.05 + -0.55x + x2 = 0 + 1.05 Combine like terms: -1.05 + 1.05 = 0.00 0.00 + -0.55x + x2 = 0 + 1.05 -0.55x + x2 = 0 + 1.05 Combine like terms: 0 + 1.05 = 1.05 -0.55x + x2 = 1.05 The x term is -0.55x. Take half its coefficient (-0.275). Square it (0.075625) and add it to both sides. Add '0.075625' to each side of the equation. -0.55x + 0.075625 + x2 = 1.05 + 0.075625 Reorder the terms: 0.075625 + -0.55x + x2 = 1.05 + 0.075625 Combine like terms: 1.05 + 0.075625 = 1.125625 0.075625 + -0.55x + x2 = 1.125625 Factor a perfect square on the left side: (x + -0.275)(x + -0.275) = 1.125625 Calculate the square root of the right side: 1.060954759 Break this problem into two subproblems by setting (x + -0.275) equal to 1.060954759 and -1.060954759.Subproblem 1
x + -0.275 = 1.060954759 Simplifying x + -0.275 = 1.060954759 Reorder the terms: -0.275 + x = 1.060954759 Solving -0.275 + x = 1.060954759 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.275' to each side of the equation. -0.275 + 0.275 + x = 1.060954759 + 0.275 Combine like terms: -0.275 + 0.275 = 0.000 0.000 + x = 1.060954759 + 0.275 x = 1.060954759 + 0.275 Combine like terms: 1.060954759 + 0.275 = 1.335954759 x = 1.335954759 Simplifying x = 1.335954759Subproblem 2
x + -0.275 = -1.060954759 Simplifying x + -0.275 = -1.060954759 Reorder the terms: -0.275 + x = -1.060954759 Solving -0.275 + x = -1.060954759 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.275' to each side of the equation. -0.275 + 0.275 + x = -1.060954759 + 0.275 Combine like terms: -0.275 + 0.275 = 0.000 0.000 + x = -1.060954759 + 0.275 x = -1.060954759 + 0.275 Combine like terms: -1.060954759 + 0.275 = -0.785954759 x = -0.785954759 Simplifying x = -0.785954759Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.335954759, -0.785954759}
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