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Simplifying 4x2 + 65x + -280 = 0 Reorder the terms: -280 + 65x + 4x2 = 0 Solving -280 + 65x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -70 + 16.25x + x2 = 0 Move the constant term to the right: Add '70' to each side of the equation. -70 + 16.25x + 70 + x2 = 0 + 70 Reorder the terms: -70 + 70 + 16.25x + x2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + 16.25x + x2 = 0 + 70 16.25x + x2 = 0 + 70 Combine like terms: 0 + 70 = 70 16.25x + x2 = 70 The x term is 16.25x. Take half its coefficient (8.125). Square it (66.015625) and add it to both sides. Add '66.015625' to each side of the equation. 16.25x + 66.015625 + x2 = 70 + 66.015625 Reorder the terms: 66.015625 + 16.25x + x2 = 70 + 66.015625 Combine like terms: 70 + 66.015625 = 136.015625 66.015625 + 16.25x + x2 = 136.015625 Factor a perfect square on the left side: (x + 8.125)(x + 8.125) = 136.015625 Calculate the square root of the right side: 11.662573687 Break this problem into two subproblems by setting (x + 8.125) equal to 11.662573687 and -11.662573687.Subproblem 1
x + 8.125 = 11.662573687 Simplifying x + 8.125 = 11.662573687 Reorder the terms: 8.125 + x = 11.662573687 Solving 8.125 + x = 11.662573687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.125' to each side of the equation. 8.125 + -8.125 + x = 11.662573687 + -8.125 Combine like terms: 8.125 + -8.125 = 0.000 0.000 + x = 11.662573687 + -8.125 x = 11.662573687 + -8.125 Combine like terms: 11.662573687 + -8.125 = 3.537573687 x = 3.537573687 Simplifying x = 3.537573687Subproblem 2
x + 8.125 = -11.662573687 Simplifying x + 8.125 = -11.662573687 Reorder the terms: 8.125 + x = -11.662573687 Solving 8.125 + x = -11.662573687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.125' to each side of the equation. 8.125 + -8.125 + x = -11.662573687 + -8.125 Combine like terms: 8.125 + -8.125 = 0.000 0.000 + x = -11.662573687 + -8.125 x = -11.662573687 + -8.125 Combine like terms: -11.662573687 + -8.125 = -19.787573687 x = -19.787573687 Simplifying x = -19.787573687Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.537573687, -19.787573687}
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