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Simplifying x2 + 19x = 11 Reorder the terms: 19x + x2 = 11 Solving 19x + x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + 19x + x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 19x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 19x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 19x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 19x + x2 = 0 + 11 19x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 19x + x2 = 11 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 = 11 + 90.25 Reorder the terms: 90.25 + 19x + x2 = 11 + 90.25 Combine like terms: 11 + 90.25 = 101.25 90.25 + 19x + x2 = 101.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 101.25 Calculate the square root of the right side: 10.062305899 Break this problem into two subproblems by setting (x + 9.5) equal to 10.062305899 and -10.062305899.Subproblem 1
x + 9.5 = 10.062305899 Simplifying x + 9.5 = 10.062305899 Reorder the terms: 9.5 + x = 10.062305899 Solving 9.5 + x = 10.062305899 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 = 10.062305899 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 10.062305899 + -9.5 x = 10.062305899 + -9.5 Combine like terms: 10.062305899 + -9.5 = 0.562305899 x = 0.562305899 Simplifying x = 0.562305899Subproblem 2
x + 9.5 = -10.062305899 Simplifying x + 9.5 = -10.062305899 Reorder the terms: 9.5 + x = -10.062305899 Solving 9.5 + x = -10.062305899 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 = -10.062305899 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -10.062305899 + -9.5 x = -10.062305899 + -9.5 Combine like terms: -10.062305899 + -9.5 = -19.562305899 x = -19.562305899 Simplifying x = -19.562305899Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.562305899, -19.562305899}
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