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Simplifying 0 = x2 + -10x + 8 Reorder the terms: 0 = 8 + -10x + x2 Solving 0 = 8 + -10x + x2 Solving for variable 'x'. Combine like terms: 0 + -8 = -8 -8 + 10x + -1x2 = 8 + -10x + x2 + -8 + 10x + -1x2 Reorder the terms: -8 + 10x + -1x2 = 8 + -8 + -10x + 10x + x2 + -1x2 Combine like terms: 8 + -8 = 0 -8 + 10x + -1x2 = 0 + -10x + 10x + x2 + -1x2 -8 + 10x + -1x2 = -10x + 10x + x2 + -1x2 Combine like terms: -10x + 10x = 0 -8 + 10x + -1x2 = 0 + x2 + -1x2 -8 + 10x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -8 + 10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 8 + -10x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -10x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -10x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -10x + x2 = 0 + -8 -10x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -10x + x2 = -8 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 = -8 + 25 Reorder the terms: 25 + -10x + x2 = -8 + 25 Combine like terms: -8 + 25 = 17 25 + -10x + x2 = 17 Factor a perfect square on the left side: (x + -5)(x + -5) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (x + -5) equal to 4.123105626 and -4.123105626.Subproblem 1
x + -5 = 4.123105626 Simplifying x + -5 = 4.123105626 Reorder the terms: -5 + x = 4.123105626 Solving -5 + x = 4.123105626 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 = 4.123105626 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.123105626 + 5 x = 4.123105626 + 5 Combine like terms: 4.123105626 + 5 = 9.123105626 x = 9.123105626 Simplifying x = 9.123105626Subproblem 2
x + -5 = -4.123105626 Simplifying x + -5 = -4.123105626 Reorder the terms: -5 + x = -4.123105626 Solving -5 + x = -4.123105626 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 = -4.123105626 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.123105626 + 5 x = -4.123105626 + 5 Combine like terms: -4.123105626 + 5 = 0.876894374 x = 0.876894374 Simplifying x = 0.876894374Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.123105626, 0.876894374}
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