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Simplifying 30 = 0.5(x + 2)(x) Reorder the terms: 30 = 0.5(2 + x)(x) Reorder the terms for easier multiplication: 30 = 0.5x(2 + x) 30 = (2 * 0.5x + x * 0.5x) 30 = (1x + 0.5x2) Solving 30 = 1x + 0.5x2 Solving for variable 'x'. Reorder the terms: 30 + -1x + -0.5x2 = 1x + -1x + 0.5x2 + -0.5x2 Combine like terms: 1x + -1x = 0 30 + -1x + -0.5x2 = 0 + 0.5x2 + -0.5x2 30 + -1x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 30 + -1x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -60 + 2x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + 2x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + 2x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 2x + x2 = 0 + 60 2x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 2x + x2 = 60 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 = 60 + 1 Reorder the terms: 1 + 2x + x2 = 60 + 1 Combine like terms: 60 + 1 = 61 1 + 2x + x2 = 61 Factor a perfect square on the left side: (x + 1)(x + 1) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (x + 1) equal to 7.810249676 and -7.810249676.Subproblem 1
x + 1 = 7.810249676 Simplifying x + 1 = 7.810249676 Reorder the terms: 1 + x = 7.810249676 Solving 1 + x = 7.810249676 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 = 7.810249676 + -1 Combine like terms: 1 + -1 = 0 0 + x = 7.810249676 + -1 x = 7.810249676 + -1 Combine like terms: 7.810249676 + -1 = 6.810249676 x = 6.810249676 Simplifying x = 6.810249676Subproblem 2
x + 1 = -7.810249676 Simplifying x + 1 = -7.810249676 Reorder the terms: 1 + x = -7.810249676 Solving 1 + x = -7.810249676 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 = -7.810249676 + -1 Combine like terms: 1 + -1 = 0 0 + x = -7.810249676 + -1 x = -7.810249676 + -1 Combine like terms: -7.810249676 + -1 = -8.810249676 x = -8.810249676 Simplifying x = -8.810249676Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.810249676, -8.810249676}
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