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Simplifying 2x2 + -121 = x Reorder the terms: -121 + 2x2 = x Solving -121 + 2x2 = x Solving for variable 'x'. Reorder the terms: -121 + -1x + 2x2 = x + -1x Combine like terms: x + -1x = 0 -121 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -60.5 + -0.5x + x2 = 0 Move the constant term to the right: Add '60.5' to each side of the equation. -60.5 + -0.5x + 60.5 + x2 = 0 + 60.5 Reorder the terms: -60.5 + 60.5 + -0.5x + x2 = 0 + 60.5 Combine like terms: -60.5 + 60.5 = 0.0 0.0 + -0.5x + x2 = 0 + 60.5 -0.5x + x2 = 0 + 60.5 Combine like terms: 0 + 60.5 = 60.5 -0.5x + x2 = 60.5 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 60.5 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 60.5 + 0.0625 Combine like terms: 60.5 + 0.0625 = 60.5625 0.0625 + -0.5x + x2 = 60.5625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 60.5625 Calculate the square root of the right side: 7.782191208 Break this problem into two subproblems by setting (x + -0.25) equal to 7.782191208 and -7.782191208.Subproblem 1
x + -0.25 = 7.782191208 Simplifying x + -0.25 = 7.782191208 Reorder the terms: -0.25 + x = 7.782191208 Solving -0.25 + x = 7.782191208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 7.782191208 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 7.782191208 + 0.25 x = 7.782191208 + 0.25 Combine like terms: 7.782191208 + 0.25 = 8.032191208 x = 8.032191208 Simplifying x = 8.032191208Subproblem 2
x + -0.25 = -7.782191208 Simplifying x + -0.25 = -7.782191208 Reorder the terms: -0.25 + x = -7.782191208 Solving -0.25 + x = -7.782191208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -7.782191208 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -7.782191208 + 0.25 x = -7.782191208 + 0.25 Combine like terms: -7.782191208 + 0.25 = -7.532191208 x = -7.532191208 Simplifying x = -7.532191208Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.032191208, -7.532191208}
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