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Simplifying 2x2 + -42x = 55 Reorder the terms: -42x + 2x2 = 55 Solving -42x + 2x2 = 55 Solving for variable 'x'. Reorder the terms: -55 + -42x + 2x2 = 55 + -55 Combine like terms: 55 + -55 = 0 -55 + -42x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -27.5 + -21x + x2 = 0 Move the constant term to the right: Add '27.5' to each side of the equation. -27.5 + -21x + 27.5 + x2 = 0 + 27.5 Reorder the terms: -27.5 + 27.5 + -21x + x2 = 0 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + -21x + x2 = 0 + 27.5 -21x + x2 = 0 + 27.5 Combine like terms: 0 + 27.5 = 27.5 -21x + x2 = 27.5 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = 27.5 + 110.25 Reorder the terms: 110.25 + -21x + x2 = 27.5 + 110.25 Combine like terms: 27.5 + 110.25 = 137.75 110.25 + -21x + x2 = 137.75 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 137.75 Calculate the square root of the right side: 11.736694594 Break this problem into two subproblems by setting (x + -10.5) equal to 11.736694594 and -11.736694594.Subproblem 1
x + -10.5 = 11.736694594 Simplifying x + -10.5 = 11.736694594 Reorder the terms: -10.5 + x = 11.736694594 Solving -10.5 + x = 11.736694594 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 11.736694594 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 11.736694594 + 10.5 x = 11.736694594 + 10.5 Combine like terms: 11.736694594 + 10.5 = 22.236694594 x = 22.236694594 Simplifying x = 22.236694594Subproblem 2
x + -10.5 = -11.736694594 Simplifying x + -10.5 = -11.736694594 Reorder the terms: -10.5 + x = -11.736694594 Solving -10.5 + x = -11.736694594 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -11.736694594 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -11.736694594 + 10.5 x = -11.736694594 + 10.5 Combine like terms: -11.736694594 + 10.5 = -1.236694594 x = -1.236694594 Simplifying x = -1.236694594Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.236694594, -1.236694594}
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