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Simplifying 0.6111x2 + -7x + -56 = 0 Reorder the terms: -56 + -7x + 0.6111x2 = 0 Solving -56 + -7x + 0.6111x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.6111 the coefficient of the squared term: Divide each side by '0.6111'. -91.63802978 + -11.45475372x + x2 = 0 Move the constant term to the right: Add '91.63802978' to each side of the equation. -91.63802978 + -11.45475372x + 91.63802978 + x2 = 0 + 91.63802978 Reorder the terms: -91.63802978 + 91.63802978 + -11.45475372x + x2 = 0 + 91.63802978 Combine like terms: -91.63802978 + 91.63802978 = 0.00000000 0.00000000 + -11.45475372x + x2 = 0 + 91.63802978 -11.45475372x + x2 = 0 + 91.63802978 Combine like terms: 0 + 91.63802978 = 91.63802978 -11.45475372x + x2 = 91.63802978 The x term is -11.45475372x. Take half its coefficient (-5.72737686). Square it (32.80284570) and add it to both sides. Add '32.80284570' to each side of the equation. -11.45475372x + 32.80284570 + x2 = 91.63802978 + 32.80284570 Reorder the terms: 32.80284570 + -11.45475372x + x2 = 91.63802978 + 32.80284570 Combine like terms: 91.63802978 + 32.80284570 = 124.44087548 32.80284570 + -11.45475372x + x2 = 124.44087548 Factor a perfect square on the left side: (x + -5.72737686)(x + -5.72737686) = 124.44087548 Calculate the square root of the right side: 11.155307054 Break this problem into two subproblems by setting (x + -5.72737686) equal to 11.155307054 and -11.155307054.Subproblem 1
x + -5.72737686 = 11.155307054 Simplifying x + -5.72737686 = 11.155307054 Reorder the terms: -5.72737686 + x = 11.155307054 Solving -5.72737686 + x = 11.155307054 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.72737686' to each side of the equation. -5.72737686 + 5.72737686 + x = 11.155307054 + 5.72737686 Combine like terms: -5.72737686 + 5.72737686 = 0.00000000 0.00000000 + x = 11.155307054 + 5.72737686 x = 11.155307054 + 5.72737686 Combine like terms: 11.155307054 + 5.72737686 = 16.882683914 x = 16.882683914 Simplifying x = 16.882683914Subproblem 2
x + -5.72737686 = -11.155307054 Simplifying x + -5.72737686 = -11.155307054 Reorder the terms: -5.72737686 + x = -11.155307054 Solving -5.72737686 + x = -11.155307054 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.72737686' to each side of the equation. -5.72737686 + 5.72737686 + x = -11.155307054 + 5.72737686 Combine like terms: -5.72737686 + 5.72737686 = 0.00000000 0.00000000 + x = -11.155307054 + 5.72737686 x = -11.155307054 + 5.72737686 Combine like terms: -11.155307054 + 5.72737686 = -5.427930194 x = -5.427930194 Simplifying x = -5.427930194Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.882683914, -5.427930194}
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