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Simplifying 2x2 + 5x = 1680 Reorder the terms: 5x + 2x2 = 1680 Solving 5x + 2x2 = 1680 Solving for variable 'x'. Reorder the terms: -1680 + 5x + 2x2 = 1680 + -1680 Combine like terms: 1680 + -1680 = 0 -1680 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -840 + 2.5x + x2 = 0 Move the constant term to the right: Add '840' to each side of the equation. -840 + 2.5x + 840 + x2 = 0 + 840 Reorder the terms: -840 + 840 + 2.5x + x2 = 0 + 840 Combine like terms: -840 + 840 = 0 0 + 2.5x + x2 = 0 + 840 2.5x + x2 = 0 + 840 Combine like terms: 0 + 840 = 840 2.5x + x2 = 840 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 840 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 840 + 1.5625 Combine like terms: 840 + 1.5625 = 841.5625 1.5625 + 2.5x + x2 = 841.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 841.5625 Calculate the square root of the right side: 29.009696655 Break this problem into two subproblems by setting (x + 1.25) equal to 29.009696655 and -29.009696655.Subproblem 1
x + 1.25 = 29.009696655 Simplifying x + 1.25 = 29.009696655 Reorder the terms: 1.25 + x = 29.009696655 Solving 1.25 + x = 29.009696655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 29.009696655 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 29.009696655 + -1.25 x = 29.009696655 + -1.25 Combine like terms: 29.009696655 + -1.25 = 27.759696655 x = 27.759696655 Simplifying x = 27.759696655Subproblem 2
x + 1.25 = -29.009696655 Simplifying x + 1.25 = -29.009696655 Reorder the terms: 1.25 + x = -29.009696655 Solving 1.25 + x = -29.009696655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -29.009696655 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -29.009696655 + -1.25 x = -29.009696655 + -1.25 Combine like terms: -29.009696655 + -1.25 = -30.259696655 x = -30.259696655 Simplifying x = -30.259696655Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.759696655, -30.259696655}
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