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Simplifying (5x + 3)(2x + 25) = 1406 Reorder the terms: (3 + 5x)(2x + 25) = 1406 Reorder the terms: (3 + 5x)(25 + 2x) = 1406 Multiply (3 + 5x) * (25 + 2x) (3(25 + 2x) + 5x * (25 + 2x)) = 1406 ((25 * 3 + 2x * 3) + 5x * (25 + 2x)) = 1406 ((75 + 6x) + 5x * (25 + 2x)) = 1406 (75 + 6x + (25 * 5x + 2x * 5x)) = 1406 (75 + 6x + (125x + 10x2)) = 1406 Combine like terms: 6x + 125x = 131x (75 + 131x + 10x2) = 1406 Solving 75 + 131x + 10x2 = 1406 Solving for variable 'x'. Reorder the terms: 75 + -1406 + 131x + 10x2 = 1406 + -1406 Combine like terms: 75 + -1406 = -1331 -1331 + 131x + 10x2 = 1406 + -1406 Combine like terms: 1406 + -1406 = 0 -1331 + 131x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -133.1 + 13.1x + x2 = 0.0 Move the constant term to the right: Add '133.1' to each side of the equation. -133.1 + 13.1x + 133.1 + x2 = 0.0 + 133.1 Reorder the terms: -133.1 + 133.1 + 13.1x + x2 = 0.0 + 133.1 Combine like terms: -133.1 + 133.1 = 0.0 0.0 + 13.1x + x2 = 0.0 + 133.1 13.1x + x2 = 0.0 + 133.1 Combine like terms: 0.0 + 133.1 = 133.1 13.1x + x2 = 133.1 The x term is 13.1x. Take half its coefficient (6.55). Square it (42.9025) and add it to both sides. Add '42.9025' to each side of the equation. 13.1x + 42.9025 + x2 = 133.1 + 42.9025 Reorder the terms: 42.9025 + 13.1x + x2 = 133.1 + 42.9025 Combine like terms: 133.1 + 42.9025 = 176.0025 42.9025 + 13.1x + x2 = 176.0025 Factor a perfect square on the left side: (x + 6.55)(x + 6.55) = 176.0025 Calculate the square root of the right side: 13.266593383 Break this problem into two subproblems by setting (x + 6.55) equal to 13.266593383 and -13.266593383.Subproblem 1
x + 6.55 = 13.266593383 Simplifying x + 6.55 = 13.266593383 Reorder the terms: 6.55 + x = 13.266593383 Solving 6.55 + x = 13.266593383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.55' to each side of the equation. 6.55 + -6.55 + x = 13.266593383 + -6.55 Combine like terms: 6.55 + -6.55 = 0.00 0.00 + x = 13.266593383 + -6.55 x = 13.266593383 + -6.55 Combine like terms: 13.266593383 + -6.55 = 6.716593383 x = 6.716593383 Simplifying x = 6.716593383Subproblem 2
x + 6.55 = -13.266593383 Simplifying x + 6.55 = -13.266593383 Reorder the terms: 6.55 + x = -13.266593383 Solving 6.55 + x = -13.266593383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.55' to each side of the equation. 6.55 + -6.55 + x = -13.266593383 + -6.55 Combine like terms: 6.55 + -6.55 = 0.00 0.00 + x = -13.266593383 + -6.55 x = -13.266593383 + -6.55 Combine like terms: -13.266593383 + -6.55 = -19.816593383 x = -19.816593383 Simplifying x = -19.816593383Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.716593383, -19.816593383}
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