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Simplifying x2 + -10x + -43 = 0 Reorder the terms: -43 + -10x + x2 = 0 Solving -43 + -10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + -10x + 43 + x2 = 0 + 43 Reorder the terms: -43 + 43 + -10x + x2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + -10x + x2 = 0 + 43 -10x + x2 = 0 + 43 Combine like terms: 0 + 43 = 43 -10x + x2 = 43 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 = 43 + 25 Reorder the terms: 25 + -10x + x2 = 43 + 25 Combine like terms: 43 + 25 = 68 25 + -10x + x2 = 68 Factor a perfect square on the left side: (x + -5)(x + -5) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (x + -5) equal to 8.246211251 and -8.246211251.Subproblem 1
x + -5 = 8.246211251 Simplifying x + -5 = 8.246211251 Reorder the terms: -5 + x = 8.246211251 Solving -5 + x = 8.246211251 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 = 8.246211251 + 5 Combine like terms: -5 + 5 = 0 0 + x = 8.246211251 + 5 x = 8.246211251 + 5 Combine like terms: 8.246211251 + 5 = 13.246211251 x = 13.246211251 Simplifying x = 13.246211251Subproblem 2
x + -5 = -8.246211251 Simplifying x + -5 = -8.246211251 Reorder the terms: -5 + x = -8.246211251 Solving -5 + x = -8.246211251 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 = -8.246211251 + 5 Combine like terms: -5 + 5 = 0 0 + x = -8.246211251 + 5 x = -8.246211251 + 5 Combine like terms: -8.246211251 + 5 = -3.246211251 x = -3.246211251 Simplifying x = -3.246211251Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.246211251, -3.246211251}
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