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Simplifying 20x2 + -10x + -3.75 = 0 Reorder the terms: -3.75 + -10x + 20x2 = 0 Solving -3.75 + -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'. -0.1875 + -0.5x + x2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -0.5x + 0.1875 + x2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -0.5x + x2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -0.5x + x2 = 0 + 0.1875 -0.5x + x2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -0.5x + x2 = 0.1875 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 = 0.1875 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 0.1875 + 0.0625 Combine like terms: 0.1875 + 0.0625 = 0.25 0.0625 + -0.5x + x2 = 0.25 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 0.25 Calculate the square root of the right side: 0.5 Break this problem into two subproblems by setting (x + -0.25) equal to 0.5 and -0.5.Subproblem 1
x + -0.25 = 0.5 Simplifying x + -0.25 = 0.5 Reorder the terms: -0.25 + x = 0.5 Solving -0.25 + x = 0.5 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 = 0.5 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.5 + 0.25 x = 0.5 + 0.25 Combine like terms: 0.5 + 0.25 = 0.75 x = 0.75 Simplifying x = 0.75Subproblem 2
x + -0.25 = -0.5 Simplifying x + -0.25 = -0.5 Reorder the terms: -0.25 + x = -0.5 Solving -0.25 + x = -0.5 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 = -0.5 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.5 + 0.25 x = -0.5 + 0.25 Combine like terms: -0.5 + 0.25 = -0.25 x = -0.25 Simplifying x = -0.25Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.75, -0.25}
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