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Simplifying 2x2 + -36x = 1 Reorder the terms: -36x + 2x2 = 1 Solving -36x + 2x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -36x + 2x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -36x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -18x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -18x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -18x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -18x + x2 = 0 + 0.5 -18x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -18x + x2 = 0.5 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = 0.5 + 81 Reorder the terms: 81 + -18x + x2 = 0.5 + 81 Combine like terms: 0.5 + 81 = 81.5 81 + -18x + x2 = 81.5 Factor a perfect square on the left side: (x + -9)(x + -9) = 81.5 Calculate the square root of the right side: 9.027735043 Break this problem into two subproblems by setting (x + -9) equal to 9.027735043 and -9.027735043.Subproblem 1
x + -9 = 9.027735043 Simplifying x + -9 = 9.027735043 Reorder the terms: -9 + x = 9.027735043 Solving -9 + x = 9.027735043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 9.027735043 + 9 Combine like terms: -9 + 9 = 0 0 + x = 9.027735043 + 9 x = 9.027735043 + 9 Combine like terms: 9.027735043 + 9 = 18.027735043 x = 18.027735043 Simplifying x = 18.027735043Subproblem 2
x + -9 = -9.027735043 Simplifying x + -9 = -9.027735043 Reorder the terms: -9 + x = -9.027735043 Solving -9 + x = -9.027735043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -9.027735043 + 9 Combine like terms: -9 + 9 = 0 0 + x = -9.027735043 + 9 x = -9.027735043 + 9 Combine like terms: -9.027735043 + 9 = -0.027735043 x = -0.027735043 Simplifying x = -0.027735043Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.027735043, -0.027735043}
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