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Simplifying 20x2 + -10x + -2.25 = 0 Reorder the terms: -2.25 + -10x + 20x2 = 0 Solving -2.25 + -10x + 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'. -0.1125 + -0.5x + x2 = 0 Move the constant term to the right: Add '0.1125' to each side of the equation. -0.1125 + -0.5x + 0.1125 + x2 = 0 + 0.1125 Reorder the terms: -0.1125 + 0.1125 + -0.5x + x2 = 0 + 0.1125 Combine like terms: -0.1125 + 0.1125 = 0.0000 0.0000 + -0.5x + x2 = 0 + 0.1125 -0.5x + x2 = 0 + 0.1125 Combine like terms: 0 + 0.1125 = 0.1125 -0.5x + x2 = 0.1125 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 0.1125 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 0.1125 + 0.0625 Combine like terms: 0.1125 + 0.0625 = 0.175 0.0625 + -0.5x + x2 = 0.175 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 0.175 Calculate the square root of the right side: 0.418330013 Break this problem into two subproblems by setting (x + -0.25) equal to 0.418330013 and -0.418330013.Subproblem 1
x + -0.25 = 0.418330013 Simplifying x + -0.25 = 0.418330013 Reorder the terms: -0.25 + x = 0.418330013 Solving -0.25 + x = 0.418330013 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 0.418330013 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.418330013 + 0.25 x = 0.418330013 + 0.25 Combine like terms: 0.418330013 + 0.25 = 0.668330013 x = 0.668330013 Simplifying x = 0.668330013Subproblem 2
x + -0.25 = -0.418330013 Simplifying x + -0.25 = -0.418330013 Reorder the terms: -0.25 + x = -0.418330013 Solving -0.25 + x = -0.418330013 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -0.418330013 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.418330013 + 0.25 x = -0.418330013 + 0.25 Combine like terms: -0.418330013 + 0.25 = -0.168330013 x = -0.168330013 Simplifying x = -0.168330013Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.668330013, -0.168330013}
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