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Simplifying (2x + 5)(x) = 5625 Reorder the terms: (5 + 2x)(x) = 5625 Reorder the terms for easier multiplication: x(5 + 2x) = 5625 (5 * x + 2x * x) = 5625 (5x + 2x2) = 5625 Solving 5x + 2x2 = 5625 Solving for variable 'x'. Reorder the terms: -5625 + 5x + 2x2 = 5625 + -5625 Combine like terms: 5625 + -5625 = 0 -5625 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2812.5 + 2.5x + x2 = 0 Move the constant term to the right: Add '2812.5' to each side of the equation. -2812.5 + 2.5x + 2812.5 + x2 = 0 + 2812.5 Reorder the terms: -2812.5 + 2812.5 + 2.5x + x2 = 0 + 2812.5 Combine like terms: -2812.5 + 2812.5 = 0.0 0.0 + 2.5x + x2 = 0 + 2812.5 2.5x + x2 = 0 + 2812.5 Combine like terms: 0 + 2812.5 = 2812.5 2.5x + x2 = 2812.5 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 = 2812.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 2812.5 + 1.5625 Combine like terms: 2812.5 + 1.5625 = 2814.0625 1.5625 + 2.5x + x2 = 2814.0625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 2814.0625 Calculate the square root of the right side: 53.047737935 Break this problem into two subproblems by setting (x + 1.25) equal to 53.047737935 and -53.047737935.Subproblem 1
x + 1.25 = 53.047737935 Simplifying x + 1.25 = 53.047737935 Reorder the terms: 1.25 + x = 53.047737935 Solving 1.25 + x = 53.047737935 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 = 53.047737935 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 53.047737935 + -1.25 x = 53.047737935 + -1.25 Combine like terms: 53.047737935 + -1.25 = 51.797737935 x = 51.797737935 Simplifying x = 51.797737935Subproblem 2
x + 1.25 = -53.047737935 Simplifying x + 1.25 = -53.047737935 Reorder the terms: 1.25 + x = -53.047737935 Solving 1.25 + x = -53.047737935 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 = -53.047737935 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -53.047737935 + -1.25 x = -53.047737935 + -1.25 Combine like terms: -53.047737935 + -1.25 = -54.297737935 x = -54.297737935 Simplifying x = -54.297737935Solution
The solution to the problem is based on the solutions from the subproblems. x = {51.797737935, -54.297737935}
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