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Simplifying 4x2 + -4x + 0.75 = 0 Reorder the terms: 0.75 + -4x + 4x2 = 0 Solving 0.75 + -4x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.1875 + -1x + x2 = 0 Move the constant term to the right: Add '-0.1875' to each side of the equation. 0.1875 + -1x + -0.1875 + x2 = 0 + -0.1875 Reorder the terms: 0.1875 + -0.1875 + -1x + x2 = 0 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + -1x + x2 = 0 + -0.1875 -1x + x2 = 0 + -0.1875 Combine like terms: 0 + -0.1875 = -0.1875 -1x + x2 = -0.1875 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -0.1875 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.1875 + 0.25 Combine like terms: -0.1875 + 0.25 = 0.0625 0.25 + -1x + x2 = 0.0625 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.0625 Calculate the square root of the right side: 0.25 Break this problem into two subproblems by setting (x + -0.5) equal to 0.25 and -0.25.Subproblem 1
x + -0.5 = 0.25 Simplifying x + -0.5 = 0.25 Reorder the terms: -0.5 + x = 0.25 Solving -0.5 + x = 0.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.25 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.25 + 0.5 x = 0.25 + 0.5 Combine like terms: 0.25 + 0.5 = 0.75 x = 0.75 Simplifying x = 0.75Subproblem 2
x + -0.5 = -0.25 Simplifying x + -0.5 = -0.25 Reorder the terms: -0.5 + x = -0.25 Solving -0.5 + x = -0.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.25 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.25 + 0.5 x = -0.25 + 0.5 Combine like terms: -0.25 + 0.5 = 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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