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Simplifying 3.93x2 + -11.35x + 3.24 = 0 Reorder the terms: 3.24 + -11.35x + 3.93x2 = 0 Solving 3.24 + -11.35x + 3.93x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.93 the coefficient of the squared term: Divide each side by '3.93'. 0.8244274809 + -2.888040712x + x2 = 0 Move the constant term to the right: Add '-0.8244274809' to each side of the equation. 0.8244274809 + -2.888040712x + -0.8244274809 + x2 = 0 + -0.8244274809 Reorder the terms: 0.8244274809 + -0.8244274809 + -2.888040712x + x2 = 0 + -0.8244274809 Combine like terms: 0.8244274809 + -0.8244274809 = 0.0000000000 0.0000000000 + -2.888040712x + x2 = 0 + -0.8244274809 -2.888040712x + x2 = 0 + -0.8244274809 Combine like terms: 0 + -0.8244274809 = -0.8244274809 -2.888040712x + x2 = -0.8244274809 The x term is -2.888040712x. Take half its coefficient (-1.444020356). Square it (2.085194789) and add it to both sides. Add '2.085194789' to each side of the equation. -2.888040712x + 2.085194789 + x2 = -0.8244274809 + 2.085194789 Reorder the terms: 2.085194789 + -2.888040712x + x2 = -0.8244274809 + 2.085194789 Combine like terms: -0.8244274809 + 2.085194789 = 1.2607673081 2.085194789 + -2.888040712x + x2 = 1.2607673081 Factor a perfect square on the left side: (x + -1.444020356)(x + -1.444020356) = 1.2607673081 Calculate the square root of the right side: 1.12283895 Break this problem into two subproblems by setting (x + -1.444020356) equal to 1.12283895 and -1.12283895.Subproblem 1
x + -1.444020356 = 1.12283895 Simplifying x + -1.444020356 = 1.12283895 Reorder the terms: -1.444020356 + x = 1.12283895 Solving -1.444020356 + x = 1.12283895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.444020356' to each side of the equation. -1.444020356 + 1.444020356 + x = 1.12283895 + 1.444020356 Combine like terms: -1.444020356 + 1.444020356 = 0.000000000 0.000000000 + x = 1.12283895 + 1.444020356 x = 1.12283895 + 1.444020356 Combine like terms: 1.12283895 + 1.444020356 = 2.566859306 x = 2.566859306 Simplifying x = 2.566859306Subproblem 2
x + -1.444020356 = -1.12283895 Simplifying x + -1.444020356 = -1.12283895 Reorder the terms: -1.444020356 + x = -1.12283895 Solving -1.444020356 + x = -1.12283895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.444020356' to each side of the equation. -1.444020356 + 1.444020356 + x = -1.12283895 + 1.444020356 Combine like terms: -1.444020356 + 1.444020356 = 0.000000000 0.000000000 + x = -1.12283895 + 1.444020356 x = -1.12283895 + 1.444020356 Combine like terms: -1.12283895 + 1.444020356 = 0.321181406 x = 0.321181406 Simplifying x = 0.321181406Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.566859306, 0.321181406}
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