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Simplifying 2x2 + 2x = 55 Reorder the terms: 2x + 2x2 = 55 Solving 2x + 2x2 = 55 Solving for variable 'x'. Reorder the terms: -55 + 2x + 2x2 = 55 + -55 Combine like terms: 55 + -55 = 0 -55 + 2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -27.5 + x + x2 = 0 Move the constant term to the right: Add '27.5' to each side of the equation. -27.5 + x + 27.5 + x2 = 0 + 27.5 Reorder the terms: -27.5 + 27.5 + x + x2 = 0 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + x + x2 = 0 + 27.5 x + x2 = 0 + 27.5 Combine like terms: 0 + 27.5 = 27.5 x + x2 = 27.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 27.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 27.5 + 0.25 Combine like terms: 27.5 + 0.25 = 27.75 1.25 + x2 = 27.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 27.75 Calculate the square root of the right side: 5.267826876 Break this problem into two subproblems by setting (x + 0.5) equal to 5.267826876 and -5.267826876.Subproblem 1
x + 0.5 = 5.267826876 Simplifying x + 0.5 = 5.267826876 Reorder the terms: 0.5 + x = 5.267826876 Solving 0.5 + x = 5.267826876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 5.267826876 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.267826876 + -0.5 x = 5.267826876 + -0.5 Combine like terms: 5.267826876 + -0.5 = 4.767826876 x = 4.767826876 Simplifying x = 4.767826876Subproblem 2
x + 0.5 = -5.267826876 Simplifying x + 0.5 = -5.267826876 Reorder the terms: 0.5 + x = -5.267826876 Solving 0.5 + x = -5.267826876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -5.267826876 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.267826876 + -0.5 x = -5.267826876 + -0.5 Combine like terms: -5.267826876 + -0.5 = -5.767826876 x = -5.767826876 Simplifying x = -5.767826876Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.767826876, -5.767826876}
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