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Simplifying 4x(2x + 5) = 5 Reorder the terms: 4x(5 + 2x) = 5 (5 * 4x + 2x * 4x) = 5 (20x + 8x2) = 5 Solving 20x + 8x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 20x + 8x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 20x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + 2.5x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 2.5x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 2.5x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 2.5x + x2 = 0 + 0.625 2.5x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 2.5x + x2 = 0.625 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 0.625 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 0.625 + 1.5625 Combine like terms: 0.625 + 1.5625 = 2.1875 1.5625 + 2.5x + x2 = 2.1875 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 2.1875 Calculate the square root of the right side: 1.479019946 Break this problem into two subproblems by setting (x + 1.25) equal to 1.479019946 and -1.479019946.Subproblem 1
x + 1.25 = 1.479019946 Simplifying x + 1.25 = 1.479019946 Reorder the terms: 1.25 + x = 1.479019946 Solving 1.25 + x = 1.479019946 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 1.479019946 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.479019946 + -1.25 x = 1.479019946 + -1.25 Combine like terms: 1.479019946 + -1.25 = 0.229019946 x = 0.229019946 Simplifying x = 0.229019946Subproblem 2
x + 1.25 = -1.479019946 Simplifying x + 1.25 = -1.479019946 Reorder the terms: 1.25 + x = -1.479019946 Solving 1.25 + x = -1.479019946 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -1.479019946 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.479019946 + -1.25 x = -1.479019946 + -1.25 Combine like terms: -1.479019946 + -1.25 = -2.729019946 x = -2.729019946 Simplifying x = -2.729019946Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.229019946, -2.729019946}
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