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Simplifying 0 = x2 + 10x + -16 Reorder the terms: 0 = -16 + 10x + x2 Solving 0 = -16 + 10x + x2 Solving for variable 'x'. Combine like terms: 0 + 16 = 16 16 + -10x + -1x2 = -16 + 10x + x2 + 16 + -10x + -1x2 Reorder the terms: 16 + -10x + -1x2 = -16 + 16 + 10x + -10x + x2 + -1x2 Combine like terms: -16 + 16 = 0 16 + -10x + -1x2 = 0 + 10x + -10x + x2 + -1x2 16 + -10x + -1x2 = 10x + -10x + x2 + -1x2 Combine like terms: 10x + -10x = 0 16 + -10x + -1x2 = 0 + x2 + -1x2 16 + -10x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 16 + -10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -16 + 10x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 10x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 10x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 10x + x2 = 0 + 16 10x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 10x + x2 = 16 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 = 16 + 25 Reorder the terms: 25 + 10x + x2 = 16 + 25 Combine like terms: 16 + 25 = 41 25 + 10x + x2 = 41 Factor a perfect square on the left side: (x + 5)(x + 5) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (x + 5) equal to 6.403124237 and -6.403124237.Subproblem 1
x + 5 = 6.403124237 Simplifying x + 5 = 6.403124237 Reorder the terms: 5 + x = 6.403124237 Solving 5 + x = 6.403124237 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 = 6.403124237 + -5 Combine like terms: 5 + -5 = 0 0 + x = 6.403124237 + -5 x = 6.403124237 + -5 Combine like terms: 6.403124237 + -5 = 1.403124237 x = 1.403124237 Simplifying x = 1.403124237Subproblem 2
x + 5 = -6.403124237 Simplifying x + 5 = -6.403124237 Reorder the terms: 5 + x = -6.403124237 Solving 5 + x = -6.403124237 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 = -6.403124237 + -5 Combine like terms: 5 + -5 = 0 0 + x = -6.403124237 + -5 x = -6.403124237 + -5 Combine like terms: -6.403124237 + -5 = -11.403124237 x = -11.403124237 Simplifying x = -11.403124237Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.403124237, -11.403124237}
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