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Simplifying 149x(22x + 139) = 5 Reorder the terms: 149x(139 + 22x) = 5 (139 * 149x + 22x * 149x) = 5 (20711x + 3278x2) = 5 Solving 20711x + 3278x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 20711x + 3278x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 20711x + 3278x2 = 0 Begin completing the square. Divide all terms by 3278 the coefficient of the squared term: Divide each side by '3278'. -0.001525320317 + 6.318181818x + x2 = 0 Move the constant term to the right: Add '0.001525320317' to each side of the equation. -0.001525320317 + 6.318181818x + 0.001525320317 + x2 = 0 + 0.001525320317 Reorder the terms: -0.001525320317 + 0.001525320317 + 6.318181818x + x2 = 0 + 0.001525320317 Combine like terms: -0.001525320317 + 0.001525320317 = 0.000000000000 0.000000000000 + 6.318181818x + x2 = 0 + 0.001525320317 6.318181818x + x2 = 0 + 0.001525320317 Combine like terms: 0 + 0.001525320317 = 0.001525320317 6.318181818x + x2 = 0.001525320317 The x term is 6.318181818x. Take half its coefficient (3.159090909). Square it (9.979855371) and add it to both sides. Add '9.979855371' to each side of the equation. 6.318181818x + 9.979855371 + x2 = 0.001525320317 + 9.979855371 Reorder the terms: 9.979855371 + 6.318181818x + x2 = 0.001525320317 + 9.979855371 Combine like terms: 0.001525320317 + 9.979855371 = 9.981380691317 9.979855371 + 6.318181818x + x2 = 9.981380691317 Factor a perfect square on the left side: (x + 3.159090909)(x + 3.159090909) = 9.981380691317 Calculate the square root of the right side: 3.159332317 Break this problem into two subproblems by setting (x + 3.159090909) equal to 3.159332317 and -3.159332317.Subproblem 1
x + 3.159090909 = 3.159332317 Simplifying x + 3.159090909 = 3.159332317 Reorder the terms: 3.159090909 + x = 3.159332317 Solving 3.159090909 + x = 3.159332317 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.159090909' to each side of the equation. 3.159090909 + -3.159090909 + x = 3.159332317 + -3.159090909 Combine like terms: 3.159090909 + -3.159090909 = 0.000000000 0.000000000 + x = 3.159332317 + -3.159090909 x = 3.159332317 + -3.159090909 Combine like terms: 3.159332317 + -3.159090909 = 0.000241408 x = 0.000241408 Simplifying x = 0.000241408Subproblem 2
x + 3.159090909 = -3.159332317 Simplifying x + 3.159090909 = -3.159332317 Reorder the terms: 3.159090909 + x = -3.159332317 Solving 3.159090909 + x = -3.159332317 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.159090909' to each side of the equation. 3.159090909 + -3.159090909 + x = -3.159332317 + -3.159090909 Combine like terms: 3.159090909 + -3.159090909 = 0.000000000 0.000000000 + x = -3.159332317 + -3.159090909 x = -3.159332317 + -3.159090909 Combine like terms: -3.159332317 + -3.159090909 = -6.318423226 x = -6.318423226 Simplifying x = -6.318423226Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.000241408, -6.318423226}
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