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Simplifying x2 + 46x + -45 = 0 Reorder the terms: -45 + 46x + x2 = 0 Solving -45 + 46x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + 46x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 46x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 46x + x2 = 0 + 45 46x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 46x + x2 = 45 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 = 45 + 529 Reorder the terms: 529 + 46x + x2 = 45 + 529 Combine like terms: 45 + 529 = 574 529 + 46x + x2 = 574 Factor a perfect square on the left side: (x + 23)(x + 23) = 574 Calculate the square root of the right side: 23.958297101 Break this problem into two subproblems by setting (x + 23) equal to 23.958297101 and -23.958297101.Subproblem 1
x + 23 = 23.958297101 Simplifying x + 23 = 23.958297101 Reorder the terms: 23 + x = 23.958297101 Solving 23 + x = 23.958297101 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 = 23.958297101 + -23 Combine like terms: 23 + -23 = 0 0 + x = 23.958297101 + -23 x = 23.958297101 + -23 Combine like terms: 23.958297101 + -23 = 0.958297101 x = 0.958297101 Simplifying x = 0.958297101Subproblem 2
x + 23 = -23.958297101 Simplifying x + 23 = -23.958297101 Reorder the terms: 23 + x = -23.958297101 Solving 23 + x = -23.958297101 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 = -23.958297101 + -23 Combine like terms: 23 + -23 = 0 0 + x = -23.958297101 + -23 x = -23.958297101 + -23 Combine like terms: -23.958297101 + -23 = -46.958297101 x = -46.958297101 Simplifying x = -46.958297101Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.958297101, -46.958297101}
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