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Simplifying 4x2 + -6x + 0.5625 = 0 Reorder the terms: 0.5625 + -6x + 4x2 = 0 Solving 0.5625 + -6x + 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'. 0.140625 + -1.5x + x2 = 0 Move the constant term to the right: Add '-0.140625' to each side of the equation. 0.140625 + -1.5x + -0.140625 + x2 = 0 + -0.140625 Reorder the terms: 0.140625 + -0.140625 + -1.5x + x2 = 0 + -0.140625 Combine like terms: 0.140625 + -0.140625 = 0.000000 0.000000 + -1.5x + x2 = 0 + -0.140625 -1.5x + x2 = 0 + -0.140625 Combine like terms: 0 + -0.140625 = -0.140625 -1.5x + x2 = -0.140625 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = -0.140625 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -0.140625 + 0.5625 Combine like terms: -0.140625 + 0.5625 = 0.421875 0.5625 + -1.5x + x2 = 0.421875 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 0.421875 Calculate the square root of the right side: 0.649519053 Break this problem into two subproblems by setting (x + -0.75) equal to 0.649519053 and -0.649519053.Subproblem 1
x + -0.75 = 0.649519053 Simplifying x + -0.75 = 0.649519053 Reorder the terms: -0.75 + x = 0.649519053 Solving -0.75 + x = 0.649519053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 0.649519053 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 0.649519053 + 0.75 x = 0.649519053 + 0.75 Combine like terms: 0.649519053 + 0.75 = 1.399519053 x = 1.399519053 Simplifying x = 1.399519053Subproblem 2
x + -0.75 = -0.649519053 Simplifying x + -0.75 = -0.649519053 Reorder the terms: -0.75 + x = -0.649519053 Solving -0.75 + x = -0.649519053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -0.649519053 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -0.649519053 + 0.75 x = -0.649519053 + 0.75 Combine like terms: -0.649519053 + 0.75 = 0.100480947 x = 0.100480947 Simplifying x = 0.100480947Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.399519053, 0.100480947}
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