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Simplifying x2 + 19x + 75 = 0 Reorder the terms: 75 + 19x + x2 = 0 Solving 75 + 19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-75' to each side of the equation. 75 + 19x + -75 + x2 = 0 + -75 Reorder the terms: 75 + -75 + 19x + x2 = 0 + -75 Combine like terms: 75 + -75 = 0 0 + 19x + x2 = 0 + -75 19x + x2 = 0 + -75 Combine like terms: 0 + -75 = -75 19x + x2 = -75 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 = -75 + 90.25 Reorder the terms: 90.25 + 19x + x2 = -75 + 90.25 Combine like terms: -75 + 90.25 = 15.25 90.25 + 19x + x2 = 15.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (x + 9.5) equal to 3.905124838 and -3.905124838.Subproblem 1
x + 9.5 = 3.905124838 Simplifying x + 9.5 = 3.905124838 Reorder the terms: 9.5 + x = 3.905124838 Solving 9.5 + x = 3.905124838 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 = 3.905124838 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 3.905124838 + -9.5 x = 3.905124838 + -9.5 Combine like terms: 3.905124838 + -9.5 = -5.594875162 x = -5.594875162 Simplifying x = -5.594875162Subproblem 2
x + 9.5 = -3.905124838 Simplifying x + 9.5 = -3.905124838 Reorder the terms: 9.5 + x = -3.905124838 Solving 9.5 + x = -3.905124838 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 = -3.905124838 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -3.905124838 + -9.5 x = -3.905124838 + -9.5 Combine like terms: -3.905124838 + -9.5 = -13.405124838 x = -13.405124838 Simplifying x = -13.405124838Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.594875162, -13.405124838}
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