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Simplifying -1x2 + 15 = 19x + -9 Reorder the terms: 15 + -1x2 = 19x + -9 Reorder the terms: 15 + -1x2 = -9 + 19x Solving 15 + -1x2 = -9 + 19x Solving for variable 'x'. Reorder the terms: 15 + 9 + -19x + -1x2 = -9 + 19x + 9 + -19x Combine like terms: 15 + 9 = 24 24 + -19x + -1x2 = -9 + 19x + 9 + -19x Reorder the terms: 24 + -19x + -1x2 = -9 + 9 + 19x + -19x Combine like terms: -9 + 9 = 0 24 + -19x + -1x2 = 0 + 19x + -19x 24 + -19x + -1x2 = 19x + -19x Combine like terms: 19x + -19x = 0 24 + -19x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -24 + 19x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 19x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 19x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 19x + x2 = 0 + 24 19x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 19x + x2 = 24 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 = 24 + 90.25 Reorder the terms: 90.25 + 19x + x2 = 24 + 90.25 Combine like terms: 24 + 90.25 = 114.25 90.25 + 19x + x2 = 114.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 114.25 Calculate the square root of the right side: 10.688779163 Break this problem into two subproblems by setting (x + 9.5) equal to 10.688779163 and -10.688779163.Subproblem 1
x + 9.5 = 10.688779163 Simplifying x + 9.5 = 10.688779163 Reorder the terms: 9.5 + x = 10.688779163 Solving 9.5 + x = 10.688779163 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 = 10.688779163 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 10.688779163 + -9.5 x = 10.688779163 + -9.5 Combine like terms: 10.688779163 + -9.5 = 1.188779163 x = 1.188779163 Simplifying x = 1.188779163Subproblem 2
x + 9.5 = -10.688779163 Simplifying x + 9.5 = -10.688779163 Reorder the terms: 9.5 + x = -10.688779163 Solving 9.5 + x = -10.688779163 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 = -10.688779163 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -10.688779163 + -9.5 x = -10.688779163 + -9.5 Combine like terms: -10.688779163 + -9.5 = -20.188779163 x = -20.188779163 Simplifying x = -20.188779163Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.188779163, -20.188779163}
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