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Simplifying 13 = 55x + -5x2 Solving 13 = 55x + -5x2 Solving for variable 'x'. Reorder the terms: 13 + -55x + 5x2 = 55x + -55x + -5x2 + 5x2 Combine like terms: 55x + -55x = 0 13 + -55x + 5x2 = 0 + -5x2 + 5x2 13 + -55x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 13 + -55x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.6 + -11x + x2 = 0 Move the constant term to the right: Add '-2.6' to each side of the equation. 2.6 + -11x + -2.6 + x2 = 0 + -2.6 Reorder the terms: 2.6 + -2.6 + -11x + x2 = 0 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + -11x + x2 = 0 + -2.6 -11x + x2 = 0 + -2.6 Combine like terms: 0 + -2.6 = -2.6 -11x + x2 = -2.6 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -2.6 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -2.6 + 30.25 Combine like terms: -2.6 + 30.25 = 27.65 30.25 + -11x + x2 = 27.65 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 27.65 Calculate the square root of the right side: 5.25832673 Break this problem into two subproblems by setting (x + -5.5) equal to 5.25832673 and -5.25832673.Subproblem 1
x + -5.5 = 5.25832673 Simplifying x + -5.5 = 5.25832673 Reorder the terms: -5.5 + x = 5.25832673 Solving -5.5 + x = 5.25832673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 5.25832673 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 5.25832673 + 5.5 x = 5.25832673 + 5.5 Combine like terms: 5.25832673 + 5.5 = 10.75832673 x = 10.75832673 Simplifying x = 10.75832673Subproblem 2
x + -5.5 = -5.25832673 Simplifying x + -5.5 = -5.25832673 Reorder the terms: -5.5 + x = -5.25832673 Solving -5.5 + x = -5.25832673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -5.25832673 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -5.25832673 + 5.5 x = -5.25832673 + 5.5 Combine like terms: -5.25832673 + 5.5 = 0.24167327 x = 0.24167327 Simplifying x = 0.24167327Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.75832673, 0.24167327}
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