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Simplifying 2x + 8 = 2x2 + 1 Reorder the terms: 8 + 2x = 2x2 + 1 Reorder the terms: 8 + 2x = 1 + 2x2 Solving 8 + 2x = 1 + 2x2 Solving for variable 'x'. Reorder the terms: 8 + -1 + 2x + -2x2 = 1 + 2x2 + -1 + -2x2 Combine like terms: 8 + -1 = 7 7 + 2x + -2x2 = 1 + 2x2 + -1 + -2x2 Reorder the terms: 7 + 2x + -2x2 = 1 + -1 + 2x2 + -2x2 Combine like terms: 1 + -1 = 0 7 + 2x + -2x2 = 0 + 2x2 + -2x2 7 + 2x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 7 + 2x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -3.5 + -1x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -1x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -1x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -1x + x2 = 0 + 3.5 -1x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -1x + x2 = 3.5 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 3.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 3.5 + 0.25 Combine like terms: 3.5 + 0.25 = 3.75 0.25 + -1x + x2 = 3.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (x + -0.5) equal to 1.936491673 and -1.936491673.Subproblem 1
x + -0.5 = 1.936491673 Simplifying x + -0.5 = 1.936491673 Reorder the terms: -0.5 + x = 1.936491673 Solving -0.5 + x = 1.936491673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.936491673 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.936491673 + 0.5 x = 1.936491673 + 0.5 Combine like terms: 1.936491673 + 0.5 = 2.436491673 x = 2.436491673 Simplifying x = 2.436491673Subproblem 2
x + -0.5 = -1.936491673 Simplifying x + -0.5 = -1.936491673 Reorder the terms: -0.5 + x = -1.936491673 Solving -0.5 + x = -1.936491673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.936491673 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.936491673 + 0.5 x = -1.936491673 + 0.5 Combine like terms: -1.936491673 + 0.5 = -1.436491673 x = -1.436491673 Simplifying x = -1.436491673Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.436491673, -1.436491673}
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