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Simplifying 0.2x2 + 4.5x + -2.8 = 0 Reorder the terms: -2.8 + 4.5x + 0.2x2 = 0 Solving -2.8 + 4.5x + 0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -14 + 22.5x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 22.5x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + 22.5x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 22.5x + x2 = 0 + 14 22.5x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 22.5x + x2 = 14 The x term is 22.5x. Take half its coefficient (11.25). Square it (126.5625) and add it to both sides. Add '126.5625' to each side of the equation. 22.5x + 126.5625 + x2 = 14 + 126.5625 Reorder the terms: 126.5625 + 22.5x + x2 = 14 + 126.5625 Combine like terms: 14 + 126.5625 = 140.5625 126.5625 + 22.5x + x2 = 140.5625 Factor a perfect square on the left side: (x + 11.25)(x + 11.25) = 140.5625 Calculate the square root of the right side: 11.855905701 Break this problem into two subproblems by setting (x + 11.25) equal to 11.855905701 and -11.855905701.Subproblem 1
x + 11.25 = 11.855905701 Simplifying x + 11.25 = 11.855905701 Reorder the terms: 11.25 + x = 11.855905701 Solving 11.25 + x = 11.855905701 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.25' to each side of the equation. 11.25 + -11.25 + x = 11.855905701 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = 11.855905701 + -11.25 x = 11.855905701 + -11.25 Combine like terms: 11.855905701 + -11.25 = 0.605905701 x = 0.605905701 Simplifying x = 0.605905701Subproblem 2
x + 11.25 = -11.855905701 Simplifying x + 11.25 = -11.855905701 Reorder the terms: 11.25 + x = -11.855905701 Solving 11.25 + x = -11.855905701 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.25' to each side of the equation. 11.25 + -11.25 + x = -11.855905701 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = -11.855905701 + -11.25 x = -11.855905701 + -11.25 Combine like terms: -11.855905701 + -11.25 = -23.105905701 x = -23.105905701 Simplifying x = -23.105905701Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.605905701, -23.105905701}
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