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Simplifying 2x * 2x + -1x = 61 Reorder the terms for easier multiplication: 2 * 2x * x + -1x = 61 Multiply 2 * 2 4x * x + -1x = 61 Multiply x * x 4x2 + -1x = 61 Reorder the terms: -1x + 4x2 = 61 Solving -1x + 4x2 = 61 Solving for variable 'x'. Reorder the terms: -61 + -1x + 4x2 = 61 + -61 Combine like terms: 61 + -61 = 0 -61 + -1x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -15.25 + -0.25x + x2 = 0 Move the constant term to the right: Add '15.25' to each side of the equation. -15.25 + -0.25x + 15.25 + x2 = 0 + 15.25 Reorder the terms: -15.25 + 15.25 + -0.25x + x2 = 0 + 15.25 Combine like terms: -15.25 + 15.25 = 0.00 0.00 + -0.25x + x2 = 0 + 15.25 -0.25x + x2 = 0 + 15.25 Combine like terms: 0 + 15.25 = 15.25 -0.25x + x2 = 15.25 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 15.25 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 15.25 + 0.015625 Combine like terms: 15.25 + 0.015625 = 15.265625 0.015625 + -0.25x + x2 = 15.265625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 15.265625 Calculate the square root of the right side: 3.907124902 Break this problem into two subproblems by setting (x + -0.125) equal to 3.907124902 and -3.907124902.Subproblem 1
x + -0.125 = 3.907124902 Simplifying x + -0.125 = 3.907124902 Reorder the terms: -0.125 + x = 3.907124902 Solving -0.125 + x = 3.907124902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 3.907124902 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 3.907124902 + 0.125 x = 3.907124902 + 0.125 Combine like terms: 3.907124902 + 0.125 = 4.032124902 x = 4.032124902 Simplifying x = 4.032124902Subproblem 2
x + -0.125 = -3.907124902 Simplifying x + -0.125 = -3.907124902 Reorder the terms: -0.125 + x = -3.907124902 Solving -0.125 + x = -3.907124902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -3.907124902 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -3.907124902 + 0.125 x = -3.907124902 + 0.125 Combine like terms: -3.907124902 + 0.125 = -3.782124902 x = -3.782124902 Simplifying x = -3.782124902Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.032124902, -3.782124902}
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