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Simplifying x2 + -19x + 61 = 0 Reorder the terms: 61 + -19x + x2 = 0 Solving 61 + -19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-61' to each side of the equation. 61 + -19x + -61 + x2 = 0 + -61 Reorder the terms: 61 + -61 + -19x + x2 = 0 + -61 Combine like terms: 61 + -61 = 0 0 + -19x + x2 = 0 + -61 -19x + x2 = 0 + -61 Combine like terms: 0 + -61 = -61 -19x + x2 = -61 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 = -61 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -61 + 90.25 Combine like terms: -61 + 90.25 = 29.25 90.25 + -19x + x2 = 29.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (x + -9.5) equal to 5.408326913 and -5.408326913.Subproblem 1
x + -9.5 = 5.408326913 Simplifying x + -9.5 = 5.408326913 Reorder the terms: -9.5 + x = 5.408326913 Solving -9.5 + x = 5.408326913 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 = 5.408326913 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 5.408326913 + 9.5 x = 5.408326913 + 9.5 Combine like terms: 5.408326913 + 9.5 = 14.908326913 x = 14.908326913 Simplifying x = 14.908326913Subproblem 2
x + -9.5 = -5.408326913 Simplifying x + -9.5 = -5.408326913 Reorder the terms: -9.5 + x = -5.408326913 Solving -9.5 + x = -5.408326913 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 = -5.408326913 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -5.408326913 + 9.5 x = -5.408326913 + 9.5 Combine like terms: -5.408326913 + 9.5 = 4.091673087 x = 4.091673087 Simplifying x = 4.091673087Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.908326913, 4.091673087}
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