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Simplifying 0.2x2 + 4.3x + -8.6 = 0 Reorder the terms: -8.6 + 4.3x + 0.2x2 = 0 Solving -8.6 + 4.3x + 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'. -43 + 21.5x + x2 = 0 Move the constant term to the right: Add '43' to each side of the equation. -43 + 21.5x + 43 + x2 = 0 + 43 Reorder the terms: -43 + 43 + 21.5x + x2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + 21.5x + x2 = 0 + 43 21.5x + x2 = 0 + 43 Combine like terms: 0 + 43 = 43 21.5x + x2 = 43 The x term is 21.5x. Take half its coefficient (10.75). Square it (115.5625) and add it to both sides. Add '115.5625' to each side of the equation. 21.5x + 115.5625 + x2 = 43 + 115.5625 Reorder the terms: 115.5625 + 21.5x + x2 = 43 + 115.5625 Combine like terms: 43 + 115.5625 = 158.5625 115.5625 + 21.5x + x2 = 158.5625 Factor a perfect square on the left side: (x + 10.75)(x + 10.75) = 158.5625 Calculate the square root of the right side: 12.592160259 Break this problem into two subproblems by setting (x + 10.75) equal to 12.592160259 and -12.592160259.Subproblem 1
x + 10.75 = 12.592160259 Simplifying x + 10.75 = 12.592160259 Reorder the terms: 10.75 + x = 12.592160259 Solving 10.75 + x = 12.592160259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.75' to each side of the equation. 10.75 + -10.75 + x = 12.592160259 + -10.75 Combine like terms: 10.75 + -10.75 = 0.00 0.00 + x = 12.592160259 + -10.75 x = 12.592160259 + -10.75 Combine like terms: 12.592160259 + -10.75 = 1.842160259 x = 1.842160259 Simplifying x = 1.842160259Subproblem 2
x + 10.75 = -12.592160259 Simplifying x + 10.75 = -12.592160259 Reorder the terms: 10.75 + x = -12.592160259 Solving 10.75 + x = -12.592160259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.75' to each side of the equation. 10.75 + -10.75 + x = -12.592160259 + -10.75 Combine like terms: 10.75 + -10.75 = 0.00 0.00 + x = -12.592160259 + -10.75 x = -12.592160259 + -10.75 Combine like terms: -12.592160259 + -10.75 = -23.342160259 x = -23.342160259 Simplifying x = -23.342160259Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.842160259, -23.342160259}
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