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Simplifying 25x(x + 1) = 5x + 4 Reorder the terms: 25x(1 + x) = 5x + 4 (1 * 25x + x * 25x) = 5x + 4 (25x + 25x2) = 5x + 4 Reorder the terms: 25x + 25x2 = 4 + 5x Solving 25x + 25x2 = 4 + 5x Solving for variable 'x'. Reorder the terms: -4 + 25x + -5x + 25x2 = 4 + 5x + -4 + -5x Combine like terms: 25x + -5x = 20x -4 + 20x + 25x2 = 4 + 5x + -4 + -5x Reorder the terms: -4 + 20x + 25x2 = 4 + -4 + 5x + -5x Combine like terms: 4 + -4 = 0 -4 + 20x + 25x2 = 0 + 5x + -5x -4 + 20x + 25x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -4 + 20x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.16 + 0.8x + x2 = 0 Move the constant term to the right: Add '0.16' to each side of the equation. -0.16 + 0.8x + 0.16 + x2 = 0 + 0.16 Reorder the terms: -0.16 + 0.16 + 0.8x + x2 = 0 + 0.16 Combine like terms: -0.16 + 0.16 = 0.00 0.00 + 0.8x + x2 = 0 + 0.16 0.8x + x2 = 0 + 0.16 Combine like terms: 0 + 0.16 = 0.16 0.8x + x2 = 0.16 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 0.16 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 0.16 + 0.16 Combine like terms: 0.16 + 0.16 = 0.32 0.16 + 0.8x + x2 = 0.32 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 0.32 Calculate the square root of the right side: 0.565685425 Break this problem into two subproblems by setting (x + 0.4) equal to 0.565685425 and -0.565685425.Subproblem 1
x + 0.4 = 0.565685425 Simplifying x + 0.4 = 0.565685425 Reorder the terms: 0.4 + x = 0.565685425 Solving 0.4 + x = 0.565685425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 0.565685425 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 0.565685425 + -0.4 x = 0.565685425 + -0.4 Combine like terms: 0.565685425 + -0.4 = 0.165685425 x = 0.165685425 Simplifying x = 0.165685425Subproblem 2
x + 0.4 = -0.565685425 Simplifying x + 0.4 = -0.565685425 Reorder the terms: 0.4 + x = -0.565685425 Solving 0.4 + x = -0.565685425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -0.565685425 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -0.565685425 + -0.4 x = -0.565685425 + -0.4 Combine like terms: -0.565685425 + -0.4 = -0.965685425 x = -0.965685425 Simplifying x = -0.965685425Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.165685425, -0.965685425}
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