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Simplifying (2x2) + 1 = 2x + 8 Reorder the terms: 1 + (2x2) = 2x + 8 Reorder the terms: 1 + (2x2) = 8 + 2x Solving 1 + (2x2) = 8 + 2x Solving for variable 'x'. Reorder the terms: 1 + -8 + -2x + (2x2) = 8 + 2x + -8 + -2x Combine like terms: 1 + -8 = -7 -7 + -2x + (2x2) = 8 + 2x + -8 + -2x Reorder the terms: -7 + -2x + (2x2) = 8 + -8 + 2x + -2x Combine like terms: 8 + -8 = 0 -7 + -2x + (2x2) = 0 + 2x + -2x -7 + -2x + (2x2) = 2x + -2x Combine like terms: 2x + -2x = 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 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 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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