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Simplifying x2 + -41x + 42 = 0 Reorder the terms: 42 + -41x + x2 = 0 Solving 42 + -41x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-42' to each side of the equation. 42 + -41x + -42 + x2 = 0 + -42 Reorder the terms: 42 + -42 + -41x + x2 = 0 + -42 Combine like terms: 42 + -42 = 0 0 + -41x + x2 = 0 + -42 -41x + x2 = 0 + -42 Combine like terms: 0 + -42 = -42 -41x + x2 = -42 The x term is -41x. Take half its coefficient (-20.5). Square it (420.25) and add it to both sides. Add '420.25' to each side of the equation. -41x + 420.25 + x2 = -42 + 420.25 Reorder the terms: 420.25 + -41x + x2 = -42 + 420.25 Combine like terms: -42 + 420.25 = 378.25 420.25 + -41x + x2 = 378.25 Factor a perfect square on the left side: (x + -20.5)(x + -20.5) = 378.25 Calculate the square root of the right side: 19.448650339 Break this problem into two subproblems by setting (x + -20.5) equal to 19.448650339 and -19.448650339.Subproblem 1
x + -20.5 = 19.448650339 Simplifying x + -20.5 = 19.448650339 Reorder the terms: -20.5 + x = 19.448650339 Solving -20.5 + x = 19.448650339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.5' to each side of the equation. -20.5 + 20.5 + x = 19.448650339 + 20.5 Combine like terms: -20.5 + 20.5 = 0.0 0.0 + x = 19.448650339 + 20.5 x = 19.448650339 + 20.5 Combine like terms: 19.448650339 + 20.5 = 39.948650339 x = 39.948650339 Simplifying x = 39.948650339Subproblem 2
x + -20.5 = -19.448650339 Simplifying x + -20.5 = -19.448650339 Reorder the terms: -20.5 + x = -19.448650339 Solving -20.5 + x = -19.448650339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.5' to each side of the equation. -20.5 + 20.5 + x = -19.448650339 + 20.5 Combine like terms: -20.5 + 20.5 = 0.0 0.0 + x = -19.448650339 + 20.5 x = -19.448650339 + 20.5 Combine like terms: -19.448650339 + 20.5 = 1.051349661 x = 1.051349661 Simplifying x = 1.051349661Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.948650339, 1.051349661}
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