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Simplifying 0.6x2 + 1.2x = 31.5 Reorder the terms: 1.2x + 0.6x2 = 31.5 Solving 1.2x + 0.6x2 = 31.5 Solving for variable 'x'. Reorder the terms: -31.5 + 1.2x + 0.6x2 = 31.5 + -31.5 Combine like terms: 31.5 + -31.5 = 0.0 -31.5 + 1.2x + 0.6x2 = 0.0 Begin completing the square. Divide all terms by 0.6 the coefficient of the squared term: Divide each side by '0.6'. -52.5 + 2x + x2 = 0 Move the constant term to the right: Add '52.5' to each side of the equation. -52.5 + 2x + 52.5 + x2 = 0 + 52.5 Reorder the terms: -52.5 + 52.5 + 2x + x2 = 0 + 52.5 Combine like terms: -52.5 + 52.5 = 0.0 0.0 + 2x + x2 = 0 + 52.5 2x + x2 = 0 + 52.5 Combine like terms: 0 + 52.5 = 52.5 2x + x2 = 52.5 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 52.5 + 1 Reorder the terms: 1 + 2x + x2 = 52.5 + 1 Combine like terms: 52.5 + 1 = 53.5 1 + 2x + x2 = 53.5 Factor a perfect square on the left side: (x + 1)(x + 1) = 53.5 Calculate the square root of the right side: 7.314369419 Break this problem into two subproblems by setting (x + 1) equal to 7.314369419 and -7.314369419.Subproblem 1
x + 1 = 7.314369419 Simplifying x + 1 = 7.314369419 Reorder the terms: 1 + x = 7.314369419 Solving 1 + x = 7.314369419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 7.314369419 + -1 Combine like terms: 1 + -1 = 0 0 + x = 7.314369419 + -1 x = 7.314369419 + -1 Combine like terms: 7.314369419 + -1 = 6.314369419 x = 6.314369419 Simplifying x = 6.314369419Subproblem 2
x + 1 = -7.314369419 Simplifying x + 1 = -7.314369419 Reorder the terms: 1 + x = -7.314369419 Solving 1 + x = -7.314369419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -7.314369419 + -1 Combine like terms: 1 + -1 = 0 0 + x = -7.314369419 + -1 x = -7.314369419 + -1 Combine like terms: -7.314369419 + -1 = -8.314369419 x = -8.314369419 Simplifying x = -8.314369419Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.314369419, -8.314369419}
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