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Simplifying 5.7x2 + -3.2x = 2 Reorder the terms: -3.2x + 5.7x2 = 2 Solving -3.2x + 5.7x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + -3.2x + 5.7x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -3.2x + 5.7x2 = 0 Begin completing the square. Divide all terms by 5.7 the coefficient of the squared term: Divide each side by '5.7'. -0.350877193 + -0.5614035088x + x2 = 0 Move the constant term to the right: Add '0.350877193' to each side of the equation. -0.350877193 + -0.5614035088x + 0.350877193 + x2 = 0 + 0.350877193 Reorder the terms: -0.350877193 + 0.350877193 + -0.5614035088x + x2 = 0 + 0.350877193 Combine like terms: -0.350877193 + 0.350877193 = 0.000000000 0.000000000 + -0.5614035088x + x2 = 0 + 0.350877193 -0.5614035088x + x2 = 0 + 0.350877193 Combine like terms: 0 + 0.350877193 = 0.350877193 -0.5614035088x + x2 = 0.350877193 The x term is -0.5614035088x. Take half its coefficient (-0.2807017544). Square it (0.07879347492) and add it to both sides. Add '0.07879347492' to each side of the equation. -0.5614035088x + 0.07879347492 + x2 = 0.350877193 + 0.07879347492 Reorder the terms: 0.07879347492 + -0.5614035088x + x2 = 0.350877193 + 0.07879347492 Combine like terms: 0.350877193 + 0.07879347492 = 0.42967066792 0.07879347492 + -0.5614035088x + x2 = 0.42967066792 Factor a perfect square on the left side: (x + -0.2807017544)(x + -0.2807017544) = 0.42967066792 Calculate the square root of the right side: 0.655492691 Break this problem into two subproblems by setting (x + -0.2807017544) equal to 0.655492691 and -0.655492691.Subproblem 1
x + -0.2807017544 = 0.655492691 Simplifying x + -0.2807017544 = 0.655492691 Reorder the terms: -0.2807017544 + x = 0.655492691 Solving -0.2807017544 + x = 0.655492691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2807017544' to each side of the equation. -0.2807017544 + 0.2807017544 + x = 0.655492691 + 0.2807017544 Combine like terms: -0.2807017544 + 0.2807017544 = 0.0000000000 0.0000000000 + x = 0.655492691 + 0.2807017544 x = 0.655492691 + 0.2807017544 Combine like terms: 0.655492691 + 0.2807017544 = 0.9361944454 x = 0.9361944454 Simplifying x = 0.9361944454Subproblem 2
x + -0.2807017544 = -0.655492691 Simplifying x + -0.2807017544 = -0.655492691 Reorder the terms: -0.2807017544 + x = -0.655492691 Solving -0.2807017544 + x = -0.655492691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2807017544' to each side of the equation. -0.2807017544 + 0.2807017544 + x = -0.655492691 + 0.2807017544 Combine like terms: -0.2807017544 + 0.2807017544 = 0.0000000000 0.0000000000 + x = -0.655492691 + 0.2807017544 x = -0.655492691 + 0.2807017544 Combine like terms: -0.655492691 + 0.2807017544 = -0.3747909366 x = -0.3747909366 Simplifying x = -0.3747909366Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9361944454, -0.3747909366}
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