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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 + -1x + x2 = 0 Move the constant term to the right: Add '6.75' to each side of the equation. -6.75 + -1x + 6.75 + x2 = 0 + 6.75 Reorder the terms: -6.75 + 6.75 + -1x + x2 = 0 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + -1x + x2 = 0 + 6.75 -1x + x2 = 0 + 6.75 Combine like terms: 0 + 6.75 = 6.75 -1x + x2 = 6.75 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 = 6.75 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 6.75 + 0.25 Combine like terms: 6.75 + 0.25 = 7 0.25 + -1x + 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 = 3.145751311 x = 3.145751311 Simplifying x = 3.145751311Subproblem 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 = -2.145751311 x = -2.145751311 Simplifying x = -2.145751311Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.145751311, -2.145751311}
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