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Simplifying 20x2 + -2x + -21 = 0 Reorder the terms: -21 + -2x + 20x2 = 0 Solving -21 + -2x + 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 + -0.1x + x2 = 0 Move the constant term to the right: Add '1.05' to each side of the equation. -1.05 + -0.1x + 1.05 + x2 = 0 + 1.05 Reorder the terms: -1.05 + 1.05 + -0.1x + x2 = 0 + 1.05 Combine like terms: -1.05 + 1.05 = 0.00 0.00 + -0.1x + x2 = 0 + 1.05 -0.1x + x2 = 0 + 1.05 Combine like terms: 0 + 1.05 = 1.05 -0.1x + x2 = 1.05 The x term is -0.1x. Take half its coefficient (-0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. -0.1x + 0.0025 + x2 = 1.05 + 0.0025 Reorder the terms: 0.0025 + -0.1x + x2 = 1.05 + 0.0025 Combine like terms: 1.05 + 0.0025 = 1.0525 0.0025 + -0.1x + x2 = 1.0525 Factor a perfect square on the left side: (x + -0.05)(x + -0.05) = 1.0525 Calculate the square root of the right side: 1.025914226 Break this problem into two subproblems by setting (x + -0.05) equal to 1.025914226 and -1.025914226.Subproblem 1
x + -0.05 = 1.025914226 Simplifying x + -0.05 = 1.025914226 Reorder the terms: -0.05 + x = 1.025914226 Solving -0.05 + x = 1.025914226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = 1.025914226 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = 1.025914226 + 0.05 x = 1.025914226 + 0.05 Combine like terms: 1.025914226 + 0.05 = 1.075914226 x = 1.075914226 Simplifying x = 1.075914226Subproblem 2
x + -0.05 = -1.025914226 Simplifying x + -0.05 = -1.025914226 Reorder the terms: -0.05 + x = -1.025914226 Solving -0.05 + x = -1.025914226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = -1.025914226 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = -1.025914226 + 0.05 x = -1.025914226 + 0.05 Combine like terms: -1.025914226 + 0.05 = -0.975914226 x = -0.975914226 Simplifying x = -0.975914226Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.075914226, -0.975914226}
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