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Simplifying x2 + -29x = 1 Reorder the terms: -29x + x2 = 1 Solving -29x + x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -29x + x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -29x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -29x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -29x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -29x + x2 = 0 + 1 -29x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -29x + x2 = 1 The x term is -29x. Take half its coefficient (-14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. -29x + 210.25 + x2 = 1 + 210.25 Reorder the terms: 210.25 + -29x + x2 = 1 + 210.25 Combine like terms: 1 + 210.25 = 211.25 210.25 + -29x + x2 = 211.25 Factor a perfect square on the left side: (x + -14.5)(x + -14.5) = 211.25 Calculate the square root of the right side: 14.534441854 Break this problem into two subproblems by setting (x + -14.5) equal to 14.534441854 and -14.534441854.Subproblem 1
x + -14.5 = 14.534441854 Simplifying x + -14.5 = 14.534441854 Reorder the terms: -14.5 + x = 14.534441854 Solving -14.5 + x = 14.534441854 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = 14.534441854 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = 14.534441854 + 14.5 x = 14.534441854 + 14.5 Combine like terms: 14.534441854 + 14.5 = 29.034441854 x = 29.034441854 Simplifying x = 29.034441854Subproblem 2
x + -14.5 = -14.534441854 Simplifying x + -14.5 = -14.534441854 Reorder the terms: -14.5 + x = -14.534441854 Solving -14.5 + x = -14.534441854 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = -14.534441854 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = -14.534441854 + 14.5 x = -14.534441854 + 14.5 Combine like terms: -14.534441854 + 14.5 = -0.034441854 x = -0.034441854 Simplifying x = -0.034441854Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.034441854, -0.034441854}
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