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Simplifying x2 + -46x + 433 = 0 Reorder the terms: 433 + -46x + x2 = 0 Solving 433 + -46x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-433' to each side of the equation. 433 + -46x + -433 + x2 = 0 + -433 Reorder the terms: 433 + -433 + -46x + x2 = 0 + -433 Combine like terms: 433 + -433 = 0 0 + -46x + x2 = 0 + -433 -46x + x2 = 0 + -433 Combine like terms: 0 + -433 = -433 -46x + x2 = -433 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 = -433 + 529 Reorder the terms: 529 + -46x + x2 = -433 + 529 Combine like terms: -433 + 529 = 96 529 + -46x + x2 = 96 Factor a perfect square on the left side: (x + -23)(x + -23) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (x + -23) equal to 9.797958971 and -9.797958971.Subproblem 1
x + -23 = 9.797958971 Simplifying x + -23 = 9.797958971 Reorder the terms: -23 + x = 9.797958971 Solving -23 + x = 9.797958971 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 = 9.797958971 + 23 Combine like terms: -23 + 23 = 0 0 + x = 9.797958971 + 23 x = 9.797958971 + 23 Combine like terms: 9.797958971 + 23 = 32.797958971 x = 32.797958971 Simplifying x = 32.797958971Subproblem 2
x + -23 = -9.797958971 Simplifying x + -23 = -9.797958971 Reorder the terms: -23 + x = -9.797958971 Solving -23 + x = -9.797958971 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 = -9.797958971 + 23 Combine like terms: -23 + 23 = 0 0 + x = -9.797958971 + 23 x = -9.797958971 + 23 Combine like terms: -9.797958971 + 23 = 13.202041029 x = 13.202041029 Simplifying x = 13.202041029Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.797958971, 13.202041029}
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