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Simplifying 5 = 4x(1 + x) 5 = (1 * 4x + x * 4x) 5 = (4x + 4x2) Solving 5 = 4x + 4x2 Solving for variable 'x'. Reorder the terms: 5 + -4x + -4x2 = 4x + -4x + 4x2 + -4x2 Combine like terms: 4x + -4x = 0 5 + -4x + -4x2 = 0 + 4x2 + -4x2 5 + -4x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 5 + -4x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.25 + x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x + x2 = 0 + 1.25 x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 x + x2 = 1.25 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 = 1.25 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 1.25 + 0.25 Combine like terms: 1.25 + 0.25 = 1.5 1.25 + x2 = 1.5 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (x + 0.5) equal to 1.224744871 and -1.224744871.Subproblem 1
x + 0.5 = 1.224744871 Simplifying x + 0.5 = 1.224744871 Reorder the terms: 0.5 + x = 1.224744871 Solving 0.5 + x = 1.224744871 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 = 1.224744871 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.224744871 + -0.5 x = 1.224744871 + -0.5 Combine like terms: 1.224744871 + -0.5 = 0.724744871 x = 0.724744871 Simplifying x = 0.724744871Subproblem 2
x + 0.5 = -1.224744871 Simplifying x + 0.5 = -1.224744871 Reorder the terms: 0.5 + x = -1.224744871 Solving 0.5 + x = -1.224744871 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 = -1.224744871 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.224744871 + -0.5 x = -1.224744871 + -0.5 Combine like terms: -1.224744871 + -0.5 = -1.724744871 x = -1.724744871 Simplifying x = -1.724744871Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.724744871, -1.724744871}
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