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Simplifying 5929 = x(x + 4) Reorder the terms: 5929 = x(4 + x) 5929 = (4 * x + x * x) 5929 = (4x + x2) Solving 5929 = 4x + x2 Solving for variable 'x'. Reorder the terms: 5929 + -4x + -1x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 5929 + -4x + -1x2 = 0 + x2 + -1x2 5929 + -4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 5929 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5929 + 4x + x2 = 0 Move the constant term to the right: Add '5929' to each side of the equation. -5929 + 4x + 5929 + x2 = 0 + 5929 Reorder the terms: -5929 + 5929 + 4x + x2 = 0 + 5929 Combine like terms: -5929 + 5929 = 0 0 + 4x + x2 = 0 + 5929 4x + x2 = 0 + 5929 Combine like terms: 0 + 5929 = 5929 4x + x2 = 5929 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 5929 + 4 Reorder the terms: 4 + 4x + x2 = 5929 + 4 Combine like terms: 5929 + 4 = 5933 4 + 4x + x2 = 5933 Factor a perfect square on the left side: (x + 2)(x + 2) = 5933 Calculate the square root of the right side: 77.025969647 Break this problem into two subproblems by setting (x + 2) equal to 77.025969647 and -77.025969647.Subproblem 1
x + 2 = 77.025969647 Simplifying x + 2 = 77.025969647 Reorder the terms: 2 + x = 77.025969647 Solving 2 + x = 77.025969647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 77.025969647 + -2 Combine like terms: 2 + -2 = 0 0 + x = 77.025969647 + -2 x = 77.025969647 + -2 Combine like terms: 77.025969647 + -2 = 75.025969647 x = 75.025969647 Simplifying x = 75.025969647Subproblem 2
x + 2 = -77.025969647 Simplifying x + 2 = -77.025969647 Reorder the terms: 2 + x = -77.025969647 Solving 2 + x = -77.025969647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -77.025969647 + -2 Combine like terms: 2 + -2 = 0 0 + x = -77.025969647 + -2 x = -77.025969647 + -2 Combine like terms: -77.025969647 + -2 = -79.025969647 x = -79.025969647 Simplifying x = -79.025969647Solution
The solution to the problem is based on the solutions from the subproblems. x = {75.025969647, -79.025969647}
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