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Simplifying 2x2 + 20x + -3375 = 0 Reorder the terms: -3375 + 20x + 2x2 = 0 Solving -3375 + 20x + 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'. -1687.5 + 10x + x2 = 0 Move the constant term to the right: Add '1687.5' to each side of the equation. -1687.5 + 10x + 1687.5 + x2 = 0 + 1687.5 Reorder the terms: -1687.5 + 1687.5 + 10x + x2 = 0 + 1687.5 Combine like terms: -1687.5 + 1687.5 = 0.0 0.0 + 10x + x2 = 0 + 1687.5 10x + x2 = 0 + 1687.5 Combine like terms: 0 + 1687.5 = 1687.5 10x + x2 = 1687.5 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 1687.5 + 25 Reorder the terms: 25 + 10x + x2 = 1687.5 + 25 Combine like terms: 1687.5 + 25 = 1712.5 25 + 10x + x2 = 1712.5 Factor a perfect square on the left side: (x + 5)(x + 5) = 1712.5 Calculate the square root of the right side: 41.382363393 Break this problem into two subproblems by setting (x + 5) equal to 41.382363393 and -41.382363393.Subproblem 1
x + 5 = 41.382363393 Simplifying x + 5 = 41.382363393 Reorder the terms: 5 + x = 41.382363393 Solving 5 + x = 41.382363393 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 41.382363393 + -5 Combine like terms: 5 + -5 = 0 0 + x = 41.382363393 + -5 x = 41.382363393 + -5 Combine like terms: 41.382363393 + -5 = 36.382363393 x = 36.382363393 Simplifying x = 36.382363393Subproblem 2
x + 5 = -41.382363393 Simplifying x + 5 = -41.382363393 Reorder the terms: 5 + x = -41.382363393 Solving 5 + x = -41.382363393 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -41.382363393 + -5 Combine like terms: 5 + -5 = 0 0 + x = -41.382363393 + -5 x = -41.382363393 + -5 Combine like terms: -41.382363393 + -5 = -46.382363393 x = -46.382363393 Simplifying x = -46.382363393Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.382363393, -46.382363393}
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