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Simplifying x2 + -19x + 80 = 0 Reorder the terms: 80 + -19x + x2 = 0 Solving 80 + -19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-80' to each side of the equation. 80 + -19x + -80 + x2 = 0 + -80 Reorder the terms: 80 + -80 + -19x + x2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + -19x + x2 = 0 + -80 -19x + x2 = 0 + -80 Combine like terms: 0 + -80 = -80 -19x + x2 = -80 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 = -80 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -80 + 90.25 Combine like terms: -80 + 90.25 = 10.25 90.25 + -19x + x2 = 10.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (x + -9.5) equal to 3.201562119 and -3.201562119.Subproblem 1
x + -9.5 = 3.201562119 Simplifying x + -9.5 = 3.201562119 Reorder the terms: -9.5 + x = 3.201562119 Solving -9.5 + x = 3.201562119 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 = 3.201562119 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 3.201562119 + 9.5 x = 3.201562119 + 9.5 Combine like terms: 3.201562119 + 9.5 = 12.701562119 x = 12.701562119 Simplifying x = 12.701562119Subproblem 2
x + -9.5 = -3.201562119 Simplifying x + -9.5 = -3.201562119 Reorder the terms: -9.5 + x = -3.201562119 Solving -9.5 + x = -3.201562119 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 = -3.201562119 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -3.201562119 + 9.5 x = -3.201562119 + 9.5 Combine like terms: -3.201562119 + 9.5 = 6.298437881 x = 6.298437881 Simplifying x = 6.298437881Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.701562119, 6.298437881}
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