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Simplifying 0 = x2 + -10x + -19 Reorder the terms: 0 = -19 + -10x + x2 Solving 0 = -19 + -10x + x2 Solving for variable 'x'. Combine like terms: 0 + 19 = 19 19 + 10x + -1x2 = -19 + -10x + x2 + 19 + 10x + -1x2 Reorder the terms: 19 + 10x + -1x2 = -19 + 19 + -10x + 10x + x2 + -1x2 Combine like terms: -19 + 19 = 0 19 + 10x + -1x2 = 0 + -10x + 10x + x2 + -1x2 19 + 10x + -1x2 = -10x + 10x + x2 + -1x2 Combine like terms: -10x + 10x = 0 19 + 10x + -1x2 = 0 + x2 + -1x2 19 + 10x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 19 + 10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -19 + -10x + x2 = 0 Move the constant term to the right: Add '19' to each side of the equation. -19 + -10x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + -10x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -10x + x2 = 0 + 19 -10x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 -10x + x2 = 19 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 = 19 + 25 Reorder the terms: 25 + -10x + x2 = 19 + 25 Combine like terms: 19 + 25 = 44 25 + -10x + x2 = 44 Factor a perfect square on the left side: (x + -5)(x + -5) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (x + -5) equal to 6.633249581 and -6.633249581.Subproblem 1
x + -5 = 6.633249581 Simplifying x + -5 = 6.633249581 Reorder the terms: -5 + x = 6.633249581 Solving -5 + x = 6.633249581 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 = 6.633249581 + 5 Combine like terms: -5 + 5 = 0 0 + x = 6.633249581 + 5 x = 6.633249581 + 5 Combine like terms: 6.633249581 + 5 = 11.633249581 x = 11.633249581 Simplifying x = 11.633249581Subproblem 2
x + -5 = -6.633249581 Simplifying x + -5 = -6.633249581 Reorder the terms: -5 + x = -6.633249581 Solving -5 + x = -6.633249581 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 = -6.633249581 + 5 Combine like terms: -5 + 5 = 0 0 + x = -6.633249581 + 5 x = -6.633249581 + 5 Combine like terms: -6.633249581 + 5 = -1.633249581 x = -1.633249581 Simplifying x = -1.633249581Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.633249581, -1.633249581}
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