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Simplifying (2x + 1)(2x + -3) = 2.5 Reorder the terms: (1 + 2x)(2x + -3) = 2.5 Reorder the terms: (1 + 2x)(-3 + 2x) = 2.5 Multiply (1 + 2x) * (-3 + 2x) (1(-3 + 2x) + 2x * (-3 + 2x)) = 2.5 ((-3 * 1 + 2x * 1) + 2x * (-3 + 2x)) = 2.5 ((-3 + 2x) + 2x * (-3 + 2x)) = 2.5 (-3 + 2x + (-3 * 2x + 2x * 2x)) = 2.5 (-3 + 2x + (-6x + 4x2)) = 2.5 Combine like terms: 2x + -6x = -4x (-3 + -4x + 4x2) = 2.5 Solving -3 + -4x + 4x2 = 2.5 Solving for variable 'x'. Reorder the terms: -3 + -2.5 + -4x + 4x2 = 2.5 + -2.5 Combine like terms: -3 + -2.5 = -5.5 -5.5 + -4x + 4x2 = 2.5 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 -5.5 + -4x + 4x2 = 0.0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.375 + -1x + x2 = 0.0 Move the constant term to the right: Add '1.375' to each side of the equation. -1.375 + -1x + 1.375 + x2 = 0.0 + 1.375 Reorder the terms: -1.375 + 1.375 + -1x + x2 = 0.0 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + -1x + x2 = 0.0 + 1.375 -1x + x2 = 0.0 + 1.375 Combine like terms: 0.0 + 1.375 = 1.375 -1x + x2 = 1.375 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 = 1.375 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 1.375 + 0.25 Combine like terms: 1.375 + 0.25 = 1.625 0.25 + -1x + x2 = 1.625 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 1.625 Calculate the square root of the right side: 1.274754878 Break this problem into two subproblems by setting (x + -0.5) equal to 1.274754878 and -1.274754878.Subproblem 1
x + -0.5 = 1.274754878 Simplifying x + -0.5 = 1.274754878 Reorder the terms: -0.5 + x = 1.274754878 Solving -0.5 + x = 1.274754878 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 = 1.274754878 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.274754878 + 0.5 x = 1.274754878 + 0.5 Combine like terms: 1.274754878 + 0.5 = 1.774754878 x = 1.774754878 Simplifying x = 1.774754878Subproblem 2
x + -0.5 = -1.274754878 Simplifying x + -0.5 = -1.274754878 Reorder the terms: -0.5 + x = -1.274754878 Solving -0.5 + x = -1.274754878 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 = -1.274754878 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.274754878 + 0.5 x = -1.274754878 + 0.5 Combine like terms: -1.274754878 + 0.5 = -0.774754878 x = -0.774754878 Simplifying x = -0.774754878Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.774754878, -0.774754878}
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