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Simplifying 2(x2 + 2x + 1) = 24 Reorder the terms: 2(1 + 2x + x2) = 24 (1 * 2 + 2x * 2 + x2 * 2) = 24 (2 + 4x + 2x2) = 24 Solving 2 + 4x + 2x2 = 24 Solving for variable 'x'. Reorder the terms: 2 + -24 + 4x + 2x2 = 24 + -24 Combine like terms: 2 + -24 = -22 -22 + 4x + 2x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -22 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-11 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-11 + 2x + x2)' equal to zero and attempt to solve: Simplifying -11 + 2x + x2 = 0 Solving -11 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 2x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 2x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 2x + x2 = 0 + 11 2x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 2x + x2 = 11 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 11 + 1 Reorder the terms: 1 + 2x + x2 = 11 + 1 Combine like terms: 11 + 1 = 12 1 + 2x + x2 = 12 Factor a perfect square on the left side: (x + 1)(x + 1) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + 1) equal to 3.464101615 and -3.464101615.Subproblem 1
x + 1 = 3.464101615 Simplifying x + 1 = 3.464101615 Reorder the terms: 1 + x = 3.464101615 Solving 1 + x = 3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 3.464101615 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.464101615 + -1 x = 3.464101615 + -1 Combine like terms: 3.464101615 + -1 = 2.464101615 x = 2.464101615 Simplifying x = 2.464101615Subproblem 2
x + 1 = -3.464101615 Simplifying x + 1 = -3.464101615 Reorder the terms: 1 + x = -3.464101615 Solving 1 + x = -3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -3.464101615 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.464101615 + -1 x = -3.464101615 + -1 Combine like terms: -3.464101615 + -1 = -4.464101615 x = -4.464101615 Simplifying x = -4.464101615Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.464101615, -4.464101615}Solution
x = {2.464101615, -4.464101615}
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