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Simplifying 0.33x2 + -0.083x + -0.25 = 0 Reorder the terms: -0.25 + -0.083x + 0.33x2 = 0 Solving -0.25 + -0.083x + 0.33x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.33 the coefficient of the squared term: Divide each side by '0.33'. -0.7575757576 + -0.2515151515x + x2 = 0 Move the constant term to the right: Add '0.7575757576' to each side of the equation. -0.7575757576 + -0.2515151515x + 0.7575757576 + x2 = 0 + 0.7575757576 Reorder the terms: -0.7575757576 + 0.7575757576 + -0.2515151515x + x2 = 0 + 0.7575757576 Combine like terms: -0.7575757576 + 0.7575757576 = 0.0000000000 0.0000000000 + -0.2515151515x + x2 = 0 + 0.7575757576 -0.2515151515x + x2 = 0 + 0.7575757576 Combine like terms: 0 + 0.7575757576 = 0.7575757576 -0.2515151515x + x2 = 0.7575757576 The x term is -0.2515151515x. Take half its coefficient (-0.1257575758). Square it (0.01581496787) and add it to both sides. Add '0.01581496787' to each side of the equation. -0.2515151515x + 0.01581496787 + x2 = 0.7575757576 + 0.01581496787 Reorder the terms: 0.01581496787 + -0.2515151515x + x2 = 0.7575757576 + 0.01581496787 Combine like terms: 0.7575757576 + 0.01581496787 = 0.77339072547 0.01581496787 + -0.2515151515x + x2 = 0.77339072547 Factor a perfect square on the left side: (x + -0.1257575758)(x + -0.1257575758) = 0.77339072547 Calculate the square root of the right side: 0.879426362 Break this problem into two subproblems by setting (x + -0.1257575758) equal to 0.879426362 and -0.879426362.Subproblem 1
x + -0.1257575758 = 0.879426362 Simplifying x + -0.1257575758 = 0.879426362 Reorder the terms: -0.1257575758 + x = 0.879426362 Solving -0.1257575758 + x = 0.879426362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1257575758' to each side of the equation. -0.1257575758 + 0.1257575758 + x = 0.879426362 + 0.1257575758 Combine like terms: -0.1257575758 + 0.1257575758 = 0.0000000000 0.0000000000 + x = 0.879426362 + 0.1257575758 x = 0.879426362 + 0.1257575758 Combine like terms: 0.879426362 + 0.1257575758 = 1.0051839378 x = 1.0051839378 Simplifying x = 1.0051839378Subproblem 2
x + -0.1257575758 = -0.879426362 Simplifying x + -0.1257575758 = -0.879426362 Reorder the terms: -0.1257575758 + x = -0.879426362 Solving -0.1257575758 + x = -0.879426362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1257575758' to each side of the equation. -0.1257575758 + 0.1257575758 + x = -0.879426362 + 0.1257575758 Combine like terms: -0.1257575758 + 0.1257575758 = 0.0000000000 0.0000000000 + x = -0.879426362 + 0.1257575758 x = -0.879426362 + 0.1257575758 Combine like terms: -0.879426362 + 0.1257575758 = -0.7536687862 x = -0.7536687862 Simplifying x = -0.7536687862Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0051839378, -0.7536687862}
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