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Simplifying 0 = x2 + 19 + -10x 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 = 6 25 + -10x + x2 = 6 Factor a perfect square on the left side: (x + -5)(x + -5) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + -5) equal to 2.449489743 and -2.449489743.Subproblem 1
x + -5 = 2.449489743 Simplifying x + -5 = 2.449489743 Reorder the terms: -5 + x = 2.449489743 Solving -5 + x = 2.449489743 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 = 2.449489743 + 5 Combine like terms: -5 + 5 = 0 0 + x = 2.449489743 + 5 x = 2.449489743 + 5 Combine like terms: 2.449489743 + 5 = 7.449489743 x = 7.449489743 Simplifying x = 7.449489743Subproblem 2
x + -5 = -2.449489743 Simplifying x + -5 = -2.449489743 Reorder the terms: -5 + x = -2.449489743 Solving -5 + x = -2.449489743 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 = -2.449489743 + 5 Combine like terms: -5 + 5 = 0 0 + x = -2.449489743 + 5 x = -2.449489743 + 5 Combine like terms: -2.449489743 + 5 = 2.550510257 x = 2.550510257 Simplifying x = 2.550510257Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.449489743, 2.550510257}
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