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Simplifying 4x2 + 325x + -2 = 43 Reorder the terms: -2 + 325x + 4x2 = 43 Solving -2 + 325x + 4x2 = 43 Solving for variable 'x'. Reorder the terms: -2 + -43 + 325x + 4x2 = 43 + -43 Combine like terms: -2 + -43 = -45 -45 + 325x + 4x2 = 43 + -43 Combine like terms: 43 + -43 = 0 -45 + 325x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -11.25 + 81.25x + x2 = 0 Move the constant term to the right: Add '11.25' to each side of the equation. -11.25 + 81.25x + 11.25 + x2 = 0 + 11.25 Reorder the terms: -11.25 + 11.25 + 81.25x + x2 = 0 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + 81.25x + x2 = 0 + 11.25 81.25x + x2 = 0 + 11.25 Combine like terms: 0 + 11.25 = 11.25 81.25x + x2 = 11.25 The x term is 81.25x. Take half its coefficient (40.625). Square it (1650.390625) and add it to both sides. Add '1650.390625' to each side of the equation. 81.25x + 1650.390625 + x2 = 11.25 + 1650.390625 Reorder the terms: 1650.390625 + 81.25x + x2 = 11.25 + 1650.390625 Combine like terms: 11.25 + 1650.390625 = 1661.640625 1650.390625 + 81.25x + x2 = 1661.640625 Factor a perfect square on the left side: (x + 40.625)(x + 40.625) = 1661.640625 Calculate the square root of the right side: 40.763226381 Break this problem into two subproblems by setting (x + 40.625) equal to 40.763226381 and -40.763226381.Subproblem 1
x + 40.625 = 40.763226381 Simplifying x + 40.625 = 40.763226381 Reorder the terms: 40.625 + x = 40.763226381 Solving 40.625 + x = 40.763226381 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40.625' to each side of the equation. 40.625 + -40.625 + x = 40.763226381 + -40.625 Combine like terms: 40.625 + -40.625 = 0.000 0.000 + x = 40.763226381 + -40.625 x = 40.763226381 + -40.625 Combine like terms: 40.763226381 + -40.625 = 0.138226381 x = 0.138226381 Simplifying x = 0.138226381Subproblem 2
x + 40.625 = -40.763226381 Simplifying x + 40.625 = -40.763226381 Reorder the terms: 40.625 + x = -40.763226381 Solving 40.625 + x = -40.763226381 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40.625' to each side of the equation. 40.625 + -40.625 + x = -40.763226381 + -40.625 Combine like terms: 40.625 + -40.625 = 0.000 0.000 + x = -40.763226381 + -40.625 x = -40.763226381 + -40.625 Combine like terms: -40.763226381 + -40.625 = -81.388226381 x = -81.388226381 Simplifying x = -81.388226381Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.138226381, -81.388226381}
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