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Simplifying 2x2 + 3x = 280 Reorder the terms: 3x + 2x2 = 280 Solving 3x + 2x2 = 280 Solving for variable 'x'. Reorder the terms: -280 + 3x + 2x2 = 280 + -280 Combine like terms: 280 + -280 = 0 -280 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -140 + 1.5x + x2 = 0 Move the constant term to the right: Add '140' to each side of the equation. -140 + 1.5x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + 1.5x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + 1.5x + x2 = 0 + 140 1.5x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 1.5x + x2 = 140 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 140 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 140 + 0.5625 Combine like terms: 140 + 0.5625 = 140.5625 0.5625 + 1.5x + x2 = 140.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 140.5625 Calculate the square root of the right side: 11.855905701 Break this problem into two subproblems by setting (x + 0.75) equal to 11.855905701 and -11.855905701.Subproblem 1
x + 0.75 = 11.855905701 Simplifying x + 0.75 = 11.855905701 Reorder the terms: 0.75 + x = 11.855905701 Solving 0.75 + x = 11.855905701 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 11.855905701 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 11.855905701 + -0.75 x = 11.855905701 + -0.75 Combine like terms: 11.855905701 + -0.75 = 11.105905701 x = 11.105905701 Simplifying x = 11.105905701Subproblem 2
x + 0.75 = -11.855905701 Simplifying x + 0.75 = -11.855905701 Reorder the terms: 0.75 + x = -11.855905701 Solving 0.75 + x = -11.855905701 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -11.855905701 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -11.855905701 + -0.75 x = -11.855905701 + -0.75 Combine like terms: -11.855905701 + -0.75 = -12.605905701 x = -12.605905701 Simplifying x = -12.605905701Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.105905701, -12.605905701}
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