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Simplifying 19 + x(10 + -1x) = 23 19 + (10 * x + -1x * x) = 23 19 + (10x + -1x2) = 23 Solving 19 + 10x + -1x2 = 23 Solving for variable 'x'. Reorder the terms: 19 + -23 + 10x + -1x2 = 23 + -23 Combine like terms: 19 + -23 = -4 -4 + 10x + -1x2 = 23 + -23 Combine like terms: 23 + -23 = 0 -4 + 10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4 + -10x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -10x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -10x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -10x + x2 = 0 + -4 -10x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -10x + x2 = -4 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 = -4 + 25 Reorder the terms: 25 + -10x + x2 = -4 + 25 Combine like terms: -4 + 25 = 21 25 + -10x + x2 = 21 Factor a perfect square on the left side: (x + -5)(x + -5) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (x + -5) equal to 4.582575695 and -4.582575695.Subproblem 1
x + -5 = 4.582575695 Simplifying x + -5 = 4.582575695 Reorder the terms: -5 + x = 4.582575695 Solving -5 + x = 4.582575695 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 = 4.582575695 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.582575695 + 5 x = 4.582575695 + 5 Combine like terms: 4.582575695 + 5 = 9.582575695 x = 9.582575695 Simplifying x = 9.582575695Subproblem 2
x + -5 = -4.582575695 Simplifying x + -5 = -4.582575695 Reorder the terms: -5 + x = -4.582575695 Solving -5 + x = -4.582575695 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 = -4.582575695 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.582575695 + 5 x = -4.582575695 + 5 Combine like terms: -4.582575695 + 5 = 0.417424305 x = 0.417424305 Simplifying x = 0.417424305Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.582575695, 0.417424305}
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