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Simplifying x2 + -46x + 50 = 0 Reorder the terms: 50 + -46x + x2 = 0 Solving 50 + -46x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-50' to each side of the equation. 50 + -46x + -50 + x2 = 0 + -50 Reorder the terms: 50 + -50 + -46x + x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -46x + x2 = 0 + -50 -46x + x2 = 0 + -50 Combine like terms: 0 + -50 = -50 -46x + x2 = -50 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 = -50 + 529 Reorder the terms: 529 + -46x + x2 = -50 + 529 Combine like terms: -50 + 529 = 479 529 + -46x + x2 = 479 Factor a perfect square on the left side: (x + -23)(x + -23) = 479 Calculate the square root of the right side: 21.886068628 Break this problem into two subproblems by setting (x + -23) equal to 21.886068628 and -21.886068628.Subproblem 1
x + -23 = 21.886068628 Simplifying x + -23 = 21.886068628 Reorder the terms: -23 + x = 21.886068628 Solving -23 + x = 21.886068628 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 = 21.886068628 + 23 Combine like terms: -23 + 23 = 0 0 + x = 21.886068628 + 23 x = 21.886068628 + 23 Combine like terms: 21.886068628 + 23 = 44.886068628 x = 44.886068628 Simplifying x = 44.886068628Subproblem 2
x + -23 = -21.886068628 Simplifying x + -23 = -21.886068628 Reorder the terms: -23 + x = -21.886068628 Solving -23 + x = -21.886068628 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 = -21.886068628 + 23 Combine like terms: -23 + 23 = 0 0 + x = -21.886068628 + 23 x = -21.886068628 + 23 Combine like terms: -21.886068628 + 23 = 1.113931372 x = 1.113931372 Simplifying x = 1.113931372Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.886068628, 1.113931372}
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