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Simplifying (2x + -1)(2x + -1) = 30 Reorder the terms: (-1 + 2x)(2x + -1) = 30 Reorder the terms: (-1 + 2x)(-1 + 2x) = 30 Multiply (-1 + 2x) * (-1 + 2x) (-1(-1 + 2x) + 2x * (-1 + 2x)) = 30 ((-1 * -1 + 2x * -1) + 2x * (-1 + 2x)) = 30 ((1 + -2x) + 2x * (-1 + 2x)) = 30 (1 + -2x + (-1 * 2x + 2x * 2x)) = 30 (1 + -2x + (-2x + 4x2)) = 30 Combine like terms: -2x + -2x = -4x (1 + -4x + 4x2) = 30 Solving 1 + -4x + 4x2 = 30 Solving for variable 'x'. Reorder the terms: 1 + -30 + -4x + 4x2 = 30 + -30 Combine like terms: 1 + -30 = -29 -29 + -4x + 4x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -29 + -4x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -7.25 + -1x + x2 = 0 Move the constant term to the right: Add '7.25' to each side of the equation. -7.25 + -1x + 7.25 + x2 = 0 + 7.25 Reorder the terms: -7.25 + 7.25 + -1x + x2 = 0 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + -1x + x2 = 0 + 7.25 -1x + x2 = 0 + 7.25 Combine like terms: 0 + 7.25 = 7.25 -1x + x2 = 7.25 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 = 7.25 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 7.25 + 0.25 Combine like terms: 7.25 + 0.25 = 7.5 0.25 + -1x + x2 = 7.5 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 7.5 Calculate the square root of the right side: 2.738612788 Break this problem into two subproblems by setting (x + -0.5) equal to 2.738612788 and -2.738612788.Subproblem 1
x + -0.5 = 2.738612788 Simplifying x + -0.5 = 2.738612788 Reorder the terms: -0.5 + x = 2.738612788 Solving -0.5 + x = 2.738612788 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 = 2.738612788 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.738612788 + 0.5 x = 2.738612788 + 0.5 Combine like terms: 2.738612788 + 0.5 = 3.238612788 x = 3.238612788 Simplifying x = 3.238612788Subproblem 2
x + -0.5 = -2.738612788 Simplifying x + -0.5 = -2.738612788 Reorder the terms: -0.5 + x = -2.738612788 Solving -0.5 + x = -2.738612788 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 = -2.738612788 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.738612788 + 0.5 x = -2.738612788 + 0.5 Combine like terms: -2.738612788 + 0.5 = -2.238612788 x = -2.238612788 Simplifying x = -2.238612788Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.238612788, -2.238612788}
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