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Simplifying 714 = (25 + 4x)(21 + 2x) Multiply (25 + 4x) * (21 + 2x) 714 = (25(21 + 2x) + 4x * (21 + 2x)) 714 = ((21 * 25 + 2x * 25) + 4x * (21 + 2x)) 714 = ((525 + 50x) + 4x * (21 + 2x)) 714 = (525 + 50x + (21 * 4x + 2x * 4x)) 714 = (525 + 50x + (84x + 8x2)) Combine like terms: 50x + 84x = 134x 714 = (525 + 134x + 8x2) Solving 714 = 525 + 134x + 8x2 Solving for variable 'x'. Combine like terms: 714 + -525 = 189 189 + -134x + -8x2 = 525 + 134x + 8x2 + -525 + -134x + -8x2 Reorder the terms: 189 + -134x + -8x2 = 525 + -525 + 134x + -134x + 8x2 + -8x2 Combine like terms: 525 + -525 = 0 189 + -134x + -8x2 = 0 + 134x + -134x + 8x2 + -8x2 189 + -134x + -8x2 = 134x + -134x + 8x2 + -8x2 Combine like terms: 134x + -134x = 0 189 + -134x + -8x2 = 0 + 8x2 + -8x2 189 + -134x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 189 + -134x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -23.625 + 16.75x + x2 = 0 Move the constant term to the right: Add '23.625' to each side of the equation. -23.625 + 16.75x + 23.625 + x2 = 0 + 23.625 Reorder the terms: -23.625 + 23.625 + 16.75x + x2 = 0 + 23.625 Combine like terms: -23.625 + 23.625 = 0.000 0.000 + 16.75x + x2 = 0 + 23.625 16.75x + x2 = 0 + 23.625 Combine like terms: 0 + 23.625 = 23.625 16.75x + x2 = 23.625 The x term is 16.75x. Take half its coefficient (8.375). Square it (70.140625) and add it to both sides. Add '70.140625' to each side of the equation. 16.75x + 70.140625 + x2 = 23.625 + 70.140625 Reorder the terms: 70.140625 + 16.75x + x2 = 23.625 + 70.140625 Combine like terms: 23.625 + 70.140625 = 93.765625 70.140625 + 16.75x + x2 = 93.765625 Factor a perfect square on the left side: (x + 8.375)(x + 8.375) = 93.765625 Calculate the square root of the right side: 9.683265203 Break this problem into two subproblems by setting (x + 8.375) equal to 9.683265203 and -9.683265203.Subproblem 1
x + 8.375 = 9.683265203 Simplifying x + 8.375 = 9.683265203 Reorder the terms: 8.375 + x = 9.683265203 Solving 8.375 + x = 9.683265203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.375' to each side of the equation. 8.375 + -8.375 + x = 9.683265203 + -8.375 Combine like terms: 8.375 + -8.375 = 0.000 0.000 + x = 9.683265203 + -8.375 x = 9.683265203 + -8.375 Combine like terms: 9.683265203 + -8.375 = 1.308265203 x = 1.308265203 Simplifying x = 1.308265203Subproblem 2
x + 8.375 = -9.683265203 Simplifying x + 8.375 = -9.683265203 Reorder the terms: 8.375 + x = -9.683265203 Solving 8.375 + x = -9.683265203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.375' to each side of the equation. 8.375 + -8.375 + x = -9.683265203 + -8.375 Combine like terms: 8.375 + -8.375 = 0.000 0.000 + x = -9.683265203 + -8.375 x = -9.683265203 + -8.375 Combine like terms: -9.683265203 + -8.375 = -18.058265203 x = -18.058265203 Simplifying x = -18.058265203Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.308265203, -18.058265203}
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