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Simplifying (2x + 1)(2x + 1) = 28 Reorder the terms: (1 + 2x)(2x + 1) = 28 Reorder the terms: (1 + 2x)(1 + 2x) = 28 Multiply (1 + 2x) * (1 + 2x) (1(1 + 2x) + 2x * (1 + 2x)) = 28 ((1 * 1 + 2x * 1) + 2x * (1 + 2x)) = 28 ((1 + 2x) + 2x * (1 + 2x)) = 28 (1 + 2x + (1 * 2x + 2x * 2x)) = 28 (1 + 2x + (2x + 4x2)) = 28 Combine like terms: 2x + 2x = 4x (1 + 4x + 4x2) = 28 Solving 1 + 4x + 4x2 = 28 Solving for variable 'x'. Reorder the terms: 1 + -28 + 4x + 4x2 = 28 + -28 Combine like terms: 1 + -28 = -27 -27 + 4x + 4x2 = 28 + -28 Combine like terms: 28 + -28 = 0 -27 + 4x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.75 + x + x2 = 0 Move the constant term to the right: Add '6.75' to each side of the equation. -6.75 + x + 6.75 + x2 = 0 + 6.75 Reorder the terms: -6.75 + 6.75 + x + x2 = 0 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x + x2 = 0 + 6.75 x + x2 = 0 + 6.75 Combine like terms: 0 + 6.75 = 6.75 x + x2 = 6.75 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. + 0.25 + x2 = 6.75 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 6.75 + 0.25 Combine like terms: 6.75 + 0.25 = 7 1.25 + x2 = 7 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + 0.5) equal to 2.645751311 and -2.645751311.Subproblem 1
x + 0.5 = 2.645751311 Simplifying x + 0.5 = 2.645751311 Reorder the terms: 0.5 + x = 2.645751311 Solving 0.5 + x = 2.645751311 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 = 2.645751311 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.645751311 + -0.5 x = 2.645751311 + -0.5 Combine like terms: 2.645751311 + -0.5 = 2.145751311 x = 2.145751311 Simplifying x = 2.145751311Subproblem 2
x + 0.5 = -2.645751311 Simplifying x + 0.5 = -2.645751311 Reorder the terms: 0.5 + x = -2.645751311 Solving 0.5 + x = -2.645751311 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 = -2.645751311 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.645751311 + -0.5 x = -2.645751311 + -0.5 Combine like terms: -2.645751311 + -0.5 = -3.145751311 x = -3.145751311 Simplifying x = -3.145751311Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.145751311, -3.145751311}
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