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Simplifying x2 + -42x + 407 = 0 Reorder the terms: 407 + -42x + x2 = 0 Solving 407 + -42x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-407' to each side of the equation. 407 + -42x + -407 + x2 = 0 + -407 Reorder the terms: 407 + -407 + -42x + x2 = 0 + -407 Combine like terms: 407 + -407 = 0 0 + -42x + x2 = 0 + -407 -42x + x2 = 0 + -407 Combine like terms: 0 + -407 = -407 -42x + x2 = -407 The x term is -42x. Take half its coefficient (-21). Square it (441) and add it to both sides. Add '441' to each side of the equation. -42x + 441 + x2 = -407 + 441 Reorder the terms: 441 + -42x + x2 = -407 + 441 Combine like terms: -407 + 441 = 34 441 + -42x + x2 = 34 Factor a perfect square on the left side: (x + -21)(x + -21) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (x + -21) equal to 5.830951895 and -5.830951895.Subproblem 1
x + -21 = 5.830951895 Simplifying x + -21 = 5.830951895 Reorder the terms: -21 + x = 5.830951895 Solving -21 + x = 5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x = 5.830951895 + 21 Combine like terms: -21 + 21 = 0 0 + x = 5.830951895 + 21 x = 5.830951895 + 21 Combine like terms: 5.830951895 + 21 = 26.830951895 x = 26.830951895 Simplifying x = 26.830951895Subproblem 2
x + -21 = -5.830951895 Simplifying x + -21 = -5.830951895 Reorder the terms: -21 + x = -5.830951895 Solving -21 + x = -5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x = -5.830951895 + 21 Combine like terms: -21 + 21 = 0 0 + x = -5.830951895 + 21 x = -5.830951895 + 21 Combine like terms: -5.830951895 + 21 = 15.169048105 x = 15.169048105 Simplifying x = 15.169048105Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.830951895, 15.169048105}
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