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Simplifying 8 = 19x + -2x2 Solving 8 = 19x + -2x2 Solving for variable 'x'. Reorder the terms: 8 + -19x + 2x2 = 19x + -19x + -2x2 + 2x2 Combine like terms: 19x + -19x = 0 8 + -19x + 2x2 = 0 + -2x2 + 2x2 8 + -19x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 8 + -19x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4 + -9.5x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -9.5x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -9.5x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -9.5x + x2 = 0 + -4 -9.5x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -9.5x + x2 = -4 The x term is -9.5x. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5x + 22.5625 + x2 = -4 + 22.5625 Reorder the terms: 22.5625 + -9.5x + x2 = -4 + 22.5625 Combine like terms: -4 + 22.5625 = 18.5625 22.5625 + -9.5x + x2 = 18.5625 Factor a perfect square on the left side: (x + -4.75)(x + -4.75) = 18.5625 Calculate the square root of the right side: 4.308421985 Break this problem into two subproblems by setting (x + -4.75) equal to 4.308421985 and -4.308421985.Subproblem 1
x + -4.75 = 4.308421985 Simplifying x + -4.75 = 4.308421985 Reorder the terms: -4.75 + x = 4.308421985 Solving -4.75 + x = 4.308421985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = 4.308421985 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 4.308421985 + 4.75 x = 4.308421985 + 4.75 Combine like terms: 4.308421985 + 4.75 = 9.058421985 x = 9.058421985 Simplifying x = 9.058421985Subproblem 2
x + -4.75 = -4.308421985 Simplifying x + -4.75 = -4.308421985 Reorder the terms: -4.75 + x = -4.308421985 Solving -4.75 + x = -4.308421985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = -4.308421985 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -4.308421985 + 4.75 x = -4.308421985 + 4.75 Combine like terms: -4.308421985 + 4.75 = 0.441578015 x = 0.441578015 Simplifying x = 0.441578015Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.058421985, 0.441578015}
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