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Simplifying x2 = 19x + 1 Reorder the terms: x2 = 1 + 19x Solving x2 = 1 + 19x Solving for variable 'x'. Reorder the terms: -1 + -19x + x2 = 1 + 19x + -1 + -19x Reorder the terms: -1 + -19x + x2 = 1 + -1 + 19x + -19x Combine like terms: 1 + -1 = 0 -1 + -19x + x2 = 0 + 19x + -19x -1 + -19x + x2 = 19x + -19x Combine like terms: 19x + -19x = 0 -1 + -19x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -19x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -19x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -19x + x2 = 0 + 1 -19x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -19x + x2 = 1 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = 1 + 90.25 Reorder the terms: 90.25 + -19x + x2 = 1 + 90.25 Combine like terms: 1 + 90.25 = 91.25 90.25 + -19x + x2 = 91.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 91.25 Calculate the square root of the right side: 9.552486587 Break this problem into two subproblems by setting (x + -9.5) equal to 9.552486587 and -9.552486587.Subproblem 1
x + -9.5 = 9.552486587 Simplifying x + -9.5 = 9.552486587 Reorder the terms: -9.5 + x = 9.552486587 Solving -9.5 + x = 9.552486587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 9.552486587 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 9.552486587 + 9.5 x = 9.552486587 + 9.5 Combine like terms: 9.552486587 + 9.5 = 19.052486587 x = 19.052486587 Simplifying x = 19.052486587Subproblem 2
x + -9.5 = -9.552486587 Simplifying x + -9.5 = -9.552486587 Reorder the terms: -9.5 + x = -9.552486587 Solving -9.5 + x = -9.552486587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -9.552486587 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -9.552486587 + 9.5 x = -9.552486587 + 9.5 Combine like terms: -9.552486587 + 9.5 = -0.052486587 x = -0.052486587 Simplifying x = -0.052486587Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.052486587, -0.052486587}
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