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Simplifying 2x2 = 8 + 5x Solving 2x2 = 8 + 5x Solving for variable 'x'. Reorder the terms: -8 + -5x + 2x2 = 8 + 5x + -8 + -5x Reorder the terms: -8 + -5x + 2x2 = 8 + -8 + 5x + -5x Combine like terms: 8 + -8 = 0 -8 + -5x + 2x2 = 0 + 5x + -5x -8 + -5x + 2x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -8 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4 + -2.5x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -2.5x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -2.5x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -2.5x + x2 = 0 + 4 -2.5x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -2.5x + x2 = 4 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 4 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 4 + 1.5625 Combine like terms: 4 + 1.5625 = 5.5625 1.5625 + -2.5x + x2 = 5.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 5.5625 Calculate the square root of the right side: 2.358495283 Break this problem into two subproblems by setting (x + -1.25) equal to 2.358495283 and -2.358495283.Subproblem 1
x + -1.25 = 2.358495283 Simplifying x + -1.25 = 2.358495283 Reorder the terms: -1.25 + x = 2.358495283 Solving -1.25 + x = 2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 2.358495283 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 2.358495283 + 1.25 x = 2.358495283 + 1.25 Combine like terms: 2.358495283 + 1.25 = 3.608495283 x = 3.608495283 Simplifying x = 3.608495283Subproblem 2
x + -1.25 = -2.358495283 Simplifying x + -1.25 = -2.358495283 Reorder the terms: -1.25 + x = -2.358495283 Solving -1.25 + x = -2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -2.358495283 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -2.358495283 + 1.25 x = -2.358495283 + 1.25 Combine like terms: -2.358495283 + 1.25 = -1.108495283 x = -1.108495283 Simplifying x = -1.108495283Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.608495283, -1.108495283}
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