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Simplifying 2x2 + 7x + -2800 = 0 Reorder the terms: -2800 + 7x + 2x2 = 0 Solving -2800 + 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'. -1400 + 3.5x + x2 = 0 Move the constant term to the right: Add '1400' to each side of the equation. -1400 + 3.5x + 1400 + x2 = 0 + 1400 Reorder the terms: -1400 + 1400 + 3.5x + x2 = 0 + 1400 Combine like terms: -1400 + 1400 = 0 0 + 3.5x + x2 = 0 + 1400 3.5x + x2 = 0 + 1400 Combine like terms: 0 + 1400 = 1400 3.5x + x2 = 1400 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 = 1400 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 1400 + 3.0625 Combine like terms: 1400 + 3.0625 = 1403.0625 3.0625 + 3.5x + x2 = 1403.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 1403.0625 Calculate the square root of the right side: 37.457475889 Break this problem into two subproblems by setting (x + 1.75) equal to 37.457475889 and -37.457475889.Subproblem 1
x + 1.75 = 37.457475889 Simplifying x + 1.75 = 37.457475889 Reorder the terms: 1.75 + x = 37.457475889 Solving 1.75 + x = 37.457475889 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 = 37.457475889 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 37.457475889 + -1.75 x = 37.457475889 + -1.75 Combine like terms: 37.457475889 + -1.75 = 35.707475889 x = 35.707475889 Simplifying x = 35.707475889Subproblem 2
x + 1.75 = -37.457475889 Simplifying x + 1.75 = -37.457475889 Reorder the terms: 1.75 + x = -37.457475889 Solving 1.75 + x = -37.457475889 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 = -37.457475889 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -37.457475889 + -1.75 x = -37.457475889 + -1.75 Combine like terms: -37.457475889 + -1.75 = -39.207475889 x = -39.207475889 Simplifying x = -39.207475889Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.707475889, -39.207475889}
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