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Simplifying 2x2 + 7x + -2500 = 0 Reorder the terms: -2500 + 7x + 2x2 = 0 Solving -2500 + 7x + 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'. -1250 + 3.5x + x2 = 0 Move the constant term to the right: Add '1250' to each side of the equation. -1250 + 3.5x + 1250 + x2 = 0 + 1250 Reorder the terms: -1250 + 1250 + 3.5x + x2 = 0 + 1250 Combine like terms: -1250 + 1250 = 0 0 + 3.5x + x2 = 0 + 1250 3.5x + x2 = 0 + 1250 Combine like terms: 0 + 1250 = 1250 3.5x + x2 = 1250 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 1250 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 1250 + 3.0625 Combine like terms: 1250 + 3.0625 = 1253.0625 3.0625 + 3.5x + x2 = 1253.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 1253.0625 Calculate the square root of the right side: 35.398622855 Break this problem into two subproblems by setting (x + 1.75) equal to 35.398622855 and -35.398622855.Subproblem 1
x + 1.75 = 35.398622855 Simplifying x + 1.75 = 35.398622855 Reorder the terms: 1.75 + x = 35.398622855 Solving 1.75 + x = 35.398622855 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 35.398622855 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 35.398622855 + -1.75 x = 35.398622855 + -1.75 Combine like terms: 35.398622855 + -1.75 = 33.648622855 x = 33.648622855 Simplifying x = 33.648622855Subproblem 2
x + 1.75 = -35.398622855 Simplifying x + 1.75 = -35.398622855 Reorder the terms: 1.75 + x = -35.398622855 Solving 1.75 + x = -35.398622855 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -35.398622855 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -35.398622855 + -1.75 x = -35.398622855 + -1.75 Combine like terms: -35.398622855 + -1.75 = -37.148622855 x = -37.148622855 Simplifying x = -37.148622855Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.648622855, -37.148622855}
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