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Simplifying 4x2 = 41 + -8x Solving 4x2 = 41 + -8x Solving for variable 'x'. Reorder the terms: -41 + 8x + 4x2 = 41 + -8x + -41 + 8x Reorder the terms: -41 + 8x + 4x2 = 41 + -41 + -8x + 8x Combine like terms: 41 + -41 = 0 -41 + 8x + 4x2 = 0 + -8x + 8x -41 + 8x + 4x2 = -8x + 8x Combine like terms: -8x + 8x = 0 -41 + 8x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -10.25 + 2x + x2 = 0 Move the constant term to the right: Add '10.25' to each side of the equation. -10.25 + 2x + 10.25 + x2 = 0 + 10.25 Reorder the terms: -10.25 + 10.25 + 2x + x2 = 0 + 10.25 Combine like terms: -10.25 + 10.25 = 0.00 0.00 + 2x + x2 = 0 + 10.25 2x + x2 = 0 + 10.25 Combine like terms: 0 + 10.25 = 10.25 2x + x2 = 10.25 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 10.25 + 1 Reorder the terms: 1 + 2x + x2 = 10.25 + 1 Combine like terms: 10.25 + 1 = 11.25 1 + 2x + x2 = 11.25 Factor a perfect square on the left side: (x + 1)(x + 1) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (x + 1) equal to 3.354101966 and -3.354101966.Subproblem 1
x + 1 = 3.354101966 Simplifying x + 1 = 3.354101966 Reorder the terms: 1 + x = 3.354101966 Solving 1 + x = 3.354101966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 3.354101966 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.354101966 + -1 x = 3.354101966 + -1 Combine like terms: 3.354101966 + -1 = 2.354101966 x = 2.354101966 Simplifying x = 2.354101966Subproblem 2
x + 1 = -3.354101966 Simplifying x + 1 = -3.354101966 Reorder the terms: 1 + x = -3.354101966 Solving 1 + x = -3.354101966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -3.354101966 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.354101966 + -1 x = -3.354101966 + -1 Combine like terms: -3.354101966 + -1 = -4.354101966 x = -4.354101966 Simplifying x = -4.354101966Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.354101966, -4.354101966}
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