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Simplifying -1x2 + 19x + 10 = 20 Reorder the terms: 10 + 19x + -1x2 = 20 Solving 10 + 19x + -1x2 = 20 Solving for variable 'x'. Reorder the terms: 10 + -20 + 19x + -1x2 = 20 + -20 Combine like terms: 10 + -20 = -10 -10 + 19x + -1x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -10 + 19x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 10 + -19x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -19x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -19x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -19x + x2 = 0 + -10 -19x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -19x + x2 = -10 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = -10 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -10 + 90.25 Combine like terms: -10 + 90.25 = 80.25 90.25 + -19x + x2 = 80.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 80.25 Calculate the square root of the right side: 8.958236434 Break this problem into two subproblems by setting (x + -9.5) equal to 8.958236434 and -8.958236434.Subproblem 1
x + -9.5 = 8.958236434 Simplifying x + -9.5 = 8.958236434 Reorder the terms: -9.5 + x = 8.958236434 Solving -9.5 + x = 8.958236434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 8.958236434 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 8.958236434 + 9.5 x = 8.958236434 + 9.5 Combine like terms: 8.958236434 + 9.5 = 18.458236434 x = 18.458236434 Simplifying x = 18.458236434Subproblem 2
x + -9.5 = -8.958236434 Simplifying x + -9.5 = -8.958236434 Reorder the terms: -9.5 + x = -8.958236434 Solving -9.5 + x = -8.958236434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -8.958236434 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -8.958236434 + 9.5 x = -8.958236434 + 9.5 Combine like terms: -8.958236434 + 9.5 = 0.541763566 x = 0.541763566 Simplifying x = 0.541763566Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.458236434, 0.541763566}
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