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Simplifying (2x + -1)(5x + 72) = 250 Reorder the terms: (-1 + 2x)(5x + 72) = 250 Reorder the terms: (-1 + 2x)(72 + 5x) = 250 Multiply (-1 + 2x) * (72 + 5x) (-1(72 + 5x) + 2x * (72 + 5x)) = 250 ((72 * -1 + 5x * -1) + 2x * (72 + 5x)) = 250 ((-72 + -5x) + 2x * (72 + 5x)) = 250 (-72 + -5x + (72 * 2x + 5x * 2x)) = 250 (-72 + -5x + (144x + 10x2)) = 250 Combine like terms: -5x + 144x = 139x (-72 + 139x + 10x2) = 250 Solving -72 + 139x + 10x2 = 250 Solving for variable 'x'. Reorder the terms: -72 + -250 + 139x + 10x2 = 250 + -250 Combine like terms: -72 + -250 = -322 -322 + 139x + 10x2 = 250 + -250 Combine like terms: 250 + -250 = 0 -322 + 139x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -32.2 + 13.9x + x2 = 0.0 Move the constant term to the right: Add '32.2' to each side of the equation. -32.2 + 13.9x + 32.2 + x2 = 0.0 + 32.2 Reorder the terms: -32.2 + 32.2 + 13.9x + x2 = 0.0 + 32.2 Combine like terms: -32.2 + 32.2 = 0.0 0.0 + 13.9x + x2 = 0.0 + 32.2 13.9x + x2 = 0.0 + 32.2 Combine like terms: 0.0 + 32.2 = 32.2 13.9x + x2 = 32.2 The x term is 13.9x. Take half its coefficient (6.95). Square it (48.3025) and add it to both sides. Add '48.3025' to each side of the equation. 13.9x + 48.3025 + x2 = 32.2 + 48.3025 Reorder the terms: 48.3025 + 13.9x + x2 = 32.2 + 48.3025 Combine like terms: 32.2 + 48.3025 = 80.5025 48.3025 + 13.9x + x2 = 80.5025 Factor a perfect square on the left side: (x + 6.95)(x + 6.95) = 80.5025 Calculate the square root of the right side: 8.972318541 Break this problem into two subproblems by setting (x + 6.95) equal to 8.972318541 and -8.972318541.Subproblem 1
x + 6.95 = 8.972318541 Simplifying x + 6.95 = 8.972318541 Reorder the terms: 6.95 + x = 8.972318541 Solving 6.95 + x = 8.972318541 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.95' to each side of the equation. 6.95 + -6.95 + x = 8.972318541 + -6.95 Combine like terms: 6.95 + -6.95 = 0.00 0.00 + x = 8.972318541 + -6.95 x = 8.972318541 + -6.95 Combine like terms: 8.972318541 + -6.95 = 2.022318541 x = 2.022318541 Simplifying x = 2.022318541Subproblem 2
x + 6.95 = -8.972318541 Simplifying x + 6.95 = -8.972318541 Reorder the terms: 6.95 + x = -8.972318541 Solving 6.95 + x = -8.972318541 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.95' to each side of the equation. 6.95 + -6.95 + x = -8.972318541 + -6.95 Combine like terms: 6.95 + -6.95 = 0.00 0.00 + x = -8.972318541 + -6.95 x = -8.972318541 + -6.95 Combine like terms: -8.972318541 + -6.95 = -15.922318541 x = -15.922318541 Simplifying x = -15.922318541Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.022318541, -15.922318541}
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