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Simplifying 2x2 + 10x + -299 = 0 Reorder the terms: -299 + 10x + 2x2 = 0 Solving -299 + 10x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -149.5 + 5x + x2 = 0 Move the constant term to the right: Add '149.5' to each side of the equation. -149.5 + 5x + 149.5 + x2 = 0 + 149.5 Reorder the terms: -149.5 + 149.5 + 5x + x2 = 0 + 149.5 Combine like terms: -149.5 + 149.5 = 0.0 0.0 + 5x + x2 = 0 + 149.5 5x + x2 = 0 + 149.5 Combine like terms: 0 + 149.5 = 149.5 5x + x2 = 149.5 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 149.5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 149.5 + 6.25 Combine like terms: 149.5 + 6.25 = 155.75 6.25 + 5x + x2 = 155.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 155.75 Calculate the square root of the right side: 12.479983974 Break this problem into two subproblems by setting (x + 2.5) equal to 12.479983974 and -12.479983974.Subproblem 1
x + 2.5 = 12.479983974 Simplifying x + 2.5 = 12.479983974 Reorder the terms: 2.5 + x = 12.479983974 Solving 2.5 + x = 12.479983974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 12.479983974 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 12.479983974 + -2.5 x = 12.479983974 + -2.5 Combine like terms: 12.479983974 + -2.5 = 9.979983974 x = 9.979983974 Simplifying x = 9.979983974Subproblem 2
x + 2.5 = -12.479983974 Simplifying x + 2.5 = -12.479983974 Reorder the terms: 2.5 + x = -12.479983974 Solving 2.5 + x = -12.479983974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -12.479983974 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -12.479983974 + -2.5 x = -12.479983974 + -2.5 Combine like terms: -12.479983974 + -2.5 = -14.979983974 x = -14.979983974 Simplifying x = -14.979983974Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.979983974, -14.979983974}
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