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Simplifying 5x2 + -108x + -228 = 0 Reorder the terms: -228 + -108x + 5x2 = 0 Solving -228 + -108x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -45.6 + -21.6x + x2 = 0 Move the constant term to the right: Add '45.6' to each side of the equation. -45.6 + -21.6x + 45.6 + x2 = 0 + 45.6 Reorder the terms: -45.6 + 45.6 + -21.6x + x2 = 0 + 45.6 Combine like terms: -45.6 + 45.6 = 0.0 0.0 + -21.6x + x2 = 0 + 45.6 -21.6x + x2 = 0 + 45.6 Combine like terms: 0 + 45.6 = 45.6 -21.6x + x2 = 45.6 The x term is -21.6x. Take half its coefficient (-10.8). Square it (116.64) and add it to both sides. Add '116.64' to each side of the equation. -21.6x + 116.64 + x2 = 45.6 + 116.64 Reorder the terms: 116.64 + -21.6x + x2 = 45.6 + 116.64 Combine like terms: 45.6 + 116.64 = 162.24 116.64 + -21.6x + x2 = 162.24 Factor a perfect square on the left side: (x + -10.8)(x + -10.8) = 162.24 Calculate the square root of the right side: 12.737346662 Break this problem into two subproblems by setting (x + -10.8) equal to 12.737346662 and -12.737346662.Subproblem 1
x + -10.8 = 12.737346662 Simplifying x + -10.8 = 12.737346662 Reorder the terms: -10.8 + x = 12.737346662 Solving -10.8 + x = 12.737346662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.8' to each side of the equation. -10.8 + 10.8 + x = 12.737346662 + 10.8 Combine like terms: -10.8 + 10.8 = 0.0 0.0 + x = 12.737346662 + 10.8 x = 12.737346662 + 10.8 Combine like terms: 12.737346662 + 10.8 = 23.537346662 x = 23.537346662 Simplifying x = 23.537346662Subproblem 2
x + -10.8 = -12.737346662 Simplifying x + -10.8 = -12.737346662 Reorder the terms: -10.8 + x = -12.737346662 Solving -10.8 + x = -12.737346662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.8' to each side of the equation. -10.8 + 10.8 + x = -12.737346662 + 10.8 Combine like terms: -10.8 + 10.8 = 0.0 0.0 + x = -12.737346662 + 10.8 x = -12.737346662 + 10.8 Combine like terms: -12.737346662 + 10.8 = -1.937346662 x = -1.937346662 Simplifying x = -1.937346662Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.537346662, -1.937346662}
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