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Simplifying x2 + -46x + 126 = 0 Reorder the terms: 126 + -46x + x2 = 0 Solving 126 + -46x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-126' to each side of the equation. 126 + -46x + -126 + x2 = 0 + -126 Reorder the terms: 126 + -126 + -46x + x2 = 0 + -126 Combine like terms: 126 + -126 = 0 0 + -46x + x2 = 0 + -126 -46x + x2 = 0 + -126 Combine like terms: 0 + -126 = -126 -46x + x2 = -126 The x term is -46x. Take half its coefficient (-23). Square it (529) and add it to both sides. Add '529' to each side of the equation. -46x + 529 + x2 = -126 + 529 Reorder the terms: 529 + -46x + x2 = -126 + 529 Combine like terms: -126 + 529 = 403 529 + -46x + x2 = 403 Factor a perfect square on the left side: (x + -23)(x + -23) = 403 Calculate the square root of the right side: 20.0748599 Break this problem into two subproblems by setting (x + -23) equal to 20.0748599 and -20.0748599.Subproblem 1
x + -23 = 20.0748599 Simplifying x + -23 = 20.0748599 Reorder the terms: -23 + x = 20.0748599 Solving -23 + x = 20.0748599 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + x = 20.0748599 + 23 Combine like terms: -23 + 23 = 0 0 + x = 20.0748599 + 23 x = 20.0748599 + 23 Combine like terms: 20.0748599 + 23 = 43.0748599 x = 43.0748599 Simplifying x = 43.0748599Subproblem 2
x + -23 = -20.0748599 Simplifying x + -23 = -20.0748599 Reorder the terms: -23 + x = -20.0748599 Solving -23 + x = -20.0748599 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + x = -20.0748599 + 23 Combine like terms: -23 + 23 = 0 0 + x = -20.0748599 + 23 x = -20.0748599 + 23 Combine like terms: -20.0748599 + 23 = 2.9251401 x = 2.9251401 Simplifying x = 2.9251401Solution
The solution to the problem is based on the solutions from the subproblems. x = {43.0748599, 2.9251401}
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