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Simplifying 2x + 11 = 2x2 + 1 Reorder the terms: 11 + 2x = 2x2 + 1 Reorder the terms: 11 + 2x = 1 + 2x2 Solving 11 + 2x = 1 + 2x2 Solving for variable 'x'. Reorder the terms: 11 + -1 + 2x + -2x2 = 1 + 2x2 + -1 + -2x2 Combine like terms: 11 + -1 = 10 10 + 2x + -2x2 = 1 + 2x2 + -1 + -2x2 Reorder the terms: 10 + 2x + -2x2 = 1 + -1 + 2x2 + -2x2 Combine like terms: 1 + -1 = 0 10 + 2x + -2x2 = 0 + 2x2 + -2x2 10 + 2x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 10 + 2x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + x + -1x2)' equal to zero and attempt to solve: Simplifying 5 + x + -1x2 = 0 Solving 5 + x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + -1x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -1x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -1x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x + x2 = 0 + 5 -1x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -1x + x2 = 5 The x term is x. 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 = 5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 5 + 0.25 Combine like terms: 5 + 0.25 = 5.25 0.25 + -1x + x2 = 5.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x + 0.5) equal to 2.291287847 and -2.291287847.Subproblem 1
x + 0.5 = 2.291287847 Simplifying x + 0.5 = 2.291287847 Reorder the terms: 0.5 + x = 2.291287847 Solving 0.5 + x = 2.291287847 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 = 2.291287847 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.291287847 + -0.5 x = 2.291287847 + -0.5 Combine like terms: 2.291287847 + -0.5 = 1.791287847 x = 1.791287847 Simplifying x = 1.791287847Subproblem 2
x + 0.5 = -2.291287847 Simplifying x + 0.5 = -2.291287847 Reorder the terms: 0.5 + x = -2.291287847 Solving 0.5 + x = -2.291287847 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 = -2.291287847 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.291287847 + -0.5 x = -2.291287847 + -0.5 Combine like terms: -2.291287847 + -0.5 = -2.791287847 x = -2.791287847 Simplifying x = -2.791287847Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.791287847, -2.791287847}Solution
x = {1.791287847, -2.791287847}
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