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Simplifying x2 + -46x + 39 = 0 Reorder the terms: 39 + -46x + x2 = 0 Solving 39 + -46x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-39' to each side of the equation. 39 + -46x + -39 + x2 = 0 + -39 Reorder the terms: 39 + -39 + -46x + x2 = 0 + -39 Combine like terms: 39 + -39 = 0 0 + -46x + x2 = 0 + -39 -46x + x2 = 0 + -39 Combine like terms: 0 + -39 = -39 -46x + x2 = -39 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 = -39 + 529 Reorder the terms: 529 + -46x + x2 = -39 + 529 Combine like terms: -39 + 529 = 490 529 + -46x + x2 = 490 Factor a perfect square on the left side: (x + -23)(x + -23) = 490 Calculate the square root of the right side: 22.135943621 Break this problem into two subproblems by setting (x + -23) equal to 22.135943621 and -22.135943621.Subproblem 1
x + -23 = 22.135943621 Simplifying x + -23 = 22.135943621 Reorder the terms: -23 + x = 22.135943621 Solving -23 + x = 22.135943621 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 = 22.135943621 + 23 Combine like terms: -23 + 23 = 0 0 + x = 22.135943621 + 23 x = 22.135943621 + 23 Combine like terms: 22.135943621 + 23 = 45.135943621 x = 45.135943621 Simplifying x = 45.135943621Subproblem 2
x + -23 = -22.135943621 Simplifying x + -23 = -22.135943621 Reorder the terms: -23 + x = -22.135943621 Solving -23 + x = -22.135943621 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 = -22.135943621 + 23 Combine like terms: -23 + 23 = 0 0 + x = -22.135943621 + 23 x = -22.135943621 + 23 Combine like terms: -22.135943621 + 23 = 0.864056379 x = 0.864056379 Simplifying x = 0.864056379Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.135943621, 0.864056379}
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