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Simplifying 8x2 = 5 + 22x Solving 8x2 = 5 + 22x Solving for variable 'x'. Reorder the terms: -5 + -22x + 8x2 = 5 + 22x + -5 + -22x Reorder the terms: -5 + -22x + 8x2 = 5 + -5 + 22x + -22x Combine like terms: 5 + -5 = 0 -5 + -22x + 8x2 = 0 + 22x + -22x -5 + -22x + 8x2 = 22x + -22x Combine like terms: 22x + -22x = 0 -5 + -22x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + -2.75x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -2.75x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -2.75x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -2.75x + x2 = 0 + 0.625 -2.75x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -2.75x + x2 = 0.625 The x term is -2.75x. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75x + 1.890625 + x2 = 0.625 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 0.625 + 1.890625 Combine like terms: 0.625 + 1.890625 = 2.515625 1.890625 + -2.75x + x2 = 2.515625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 2.515625 Calculate the square root of the right side: 1.586072193 Break this problem into two subproblems by setting (x + -1.375) equal to 1.586072193 and -1.586072193.Subproblem 1
x + -1.375 = 1.586072193 Simplifying x + -1.375 = 1.586072193 Reorder the terms: -1.375 + x = 1.586072193 Solving -1.375 + x = 1.586072193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = 1.586072193 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 1.586072193 + 1.375 x = 1.586072193 + 1.375 Combine like terms: 1.586072193 + 1.375 = 2.961072193 x = 2.961072193 Simplifying x = 2.961072193Subproblem 2
x + -1.375 = -1.586072193 Simplifying x + -1.375 = -1.586072193 Reorder the terms: -1.375 + x = -1.586072193 Solving -1.375 + x = -1.586072193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = -1.586072193 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -1.586072193 + 1.375 x = -1.586072193 + 1.375 Combine like terms: -1.586072193 + 1.375 = -0.211072193 x = -0.211072193 Simplifying x = -0.211072193Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.961072193, -0.211072193}
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