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Simplifying x2 + -10x + -4 = 10 Reorder the terms: -4 + -10x + x2 = 10 Solving -4 + -10x + x2 = 10 Solving for variable 'x'. Reorder the terms: -4 + -10 + -10x + x2 = 10 + -10 Combine like terms: -4 + -10 = -14 -14 + -10x + x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -14 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -10x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + -10x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -10x + x2 = 0 + 14 -10x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 -10x + x2 = 14 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 = 14 + 25 Reorder the terms: 25 + -10x + x2 = 14 + 25 Combine like terms: 14 + 25 = 39 25 + -10x + x2 = 39 Factor a perfect square on the left side: (x + -5)(x + -5) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (x + -5) equal to 6.244997998 and -6.244997998.Subproblem 1
x + -5 = 6.244997998 Simplifying x + -5 = 6.244997998 Reorder the terms: -5 + x = 6.244997998 Solving -5 + x = 6.244997998 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 = 6.244997998 + 5 Combine like terms: -5 + 5 = 0 0 + x = 6.244997998 + 5 x = 6.244997998 + 5 Combine like terms: 6.244997998 + 5 = 11.244997998 x = 11.244997998 Simplifying x = 11.244997998Subproblem 2
x + -5 = -6.244997998 Simplifying x + -5 = -6.244997998 Reorder the terms: -5 + x = -6.244997998 Solving -5 + x = -6.244997998 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 = -6.244997998 + 5 Combine like terms: -5 + 5 = 0 0 + x = -6.244997998 + 5 x = -6.244997998 + 5 Combine like terms: -6.244997998 + 5 = -1.244997998 x = -1.244997998 Simplifying x = -1.244997998Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.244997998, -1.244997998}
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