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Simplifying 4.57x2 + -10.69x + 2.99 = 0 Reorder the terms: 2.99 + -10.69x + 4.57x2 = 0 Solving 2.99 + -10.69x + 4.57x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.57 the coefficient of the squared term: Divide each side by '4.57'. 0.6542669584 + -2.33916849x + x2 = 0 Move the constant term to the right: Add '-0.6542669584' to each side of the equation. 0.6542669584 + -2.33916849x + -0.6542669584 + x2 = 0 + -0.6542669584 Reorder the terms: 0.6542669584 + -0.6542669584 + -2.33916849x + x2 = 0 + -0.6542669584 Combine like terms: 0.6542669584 + -0.6542669584 = 0.0000000000 0.0000000000 + -2.33916849x + x2 = 0 + -0.6542669584 -2.33916849x + x2 = 0 + -0.6542669584 Combine like terms: 0 + -0.6542669584 = -0.6542669584 -2.33916849x + x2 = -0.6542669584 The x term is -2.33916849x. Take half its coefficient (-1.169584245). Square it (1.367927306) and add it to both sides. Add '1.367927306' to each side of the equation. -2.33916849x + 1.367927306 + x2 = -0.6542669584 + 1.367927306 Reorder the terms: 1.367927306 + -2.33916849x + x2 = -0.6542669584 + 1.367927306 Combine like terms: -0.6542669584 + 1.367927306 = 0.7136603476 1.367927306 + -2.33916849x + x2 = 0.7136603476 Factor a perfect square on the left side: (x + -1.169584245)(x + -1.169584245) = 0.7136603476 Calculate the square root of the right side: 0.844784202 Break this problem into two subproblems by setting (x + -1.169584245) equal to 0.844784202 and -0.844784202.Subproblem 1
x + -1.169584245 = 0.844784202 Simplifying x + -1.169584245 = 0.844784202 Reorder the terms: -1.169584245 + x = 0.844784202 Solving -1.169584245 + x = 0.844784202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.169584245' to each side of the equation. -1.169584245 + 1.169584245 + x = 0.844784202 + 1.169584245 Combine like terms: -1.169584245 + 1.169584245 = 0.000000000 0.000000000 + x = 0.844784202 + 1.169584245 x = 0.844784202 + 1.169584245 Combine like terms: 0.844784202 + 1.169584245 = 2.014368447 x = 2.014368447 Simplifying x = 2.014368447Subproblem 2
x + -1.169584245 = -0.844784202 Simplifying x + -1.169584245 = -0.844784202 Reorder the terms: -1.169584245 + x = -0.844784202 Solving -1.169584245 + x = -0.844784202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.169584245' to each side of the equation. -1.169584245 + 1.169584245 + x = -0.844784202 + 1.169584245 Combine like terms: -1.169584245 + 1.169584245 = 0.000000000 0.000000000 + x = -0.844784202 + 1.169584245 x = -0.844784202 + 1.169584245 Combine like terms: -0.844784202 + 1.169584245 = 0.324800043 x = 0.324800043 Simplifying x = 0.324800043Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.014368447, 0.324800043}
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