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Simplifying x2 + -10x = 46 Reorder the terms: -10x + x2 = 46 Solving -10x + x2 = 46 Solving for variable 'x'. Reorder the terms: -46 + -10x + x2 = 46 + -46 Combine like terms: 46 + -46 = 0 -46 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '46' to each side of the equation. -46 + -10x + 46 + x2 = 0 + 46 Reorder the terms: -46 + 46 + -10x + x2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + -10x + x2 = 0 + 46 -10x + x2 = 0 + 46 Combine like terms: 0 + 46 = 46 -10x + x2 = 46 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 46 + 25 Reorder the terms: 25 + -10x + x2 = 46 + 25 Combine like terms: 46 + 25 = 71 25 + -10x + x2 = 71 Factor a perfect square on the left side: (x + -5)(x + -5) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (x + -5) equal to 8.426149773 and -8.426149773.Subproblem 1
x + -5 = 8.426149773 Simplifying x + -5 = 8.426149773 Reorder the terms: -5 + x = 8.426149773 Solving -5 + x = 8.426149773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 8.426149773 + 5 Combine like terms: -5 + 5 = 0 0 + x = 8.426149773 + 5 x = 8.426149773 + 5 Combine like terms: 8.426149773 + 5 = 13.426149773 x = 13.426149773 Simplifying x = 13.426149773Subproblem 2
x + -5 = -8.426149773 Simplifying x + -5 = -8.426149773 Reorder the terms: -5 + x = -8.426149773 Solving -5 + x = -8.426149773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -8.426149773 + 5 Combine like terms: -5 + 5 = 0 0 + x = -8.426149773 + 5 x = -8.426149773 + 5 Combine like terms: -8.426149773 + 5 = -3.426149773 x = -3.426149773 Simplifying x = -3.426149773Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.426149773, -3.426149773}
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