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Simplifying x2 + 19x + 15 = 0 Reorder the terms: 15 + 19x + x2 = 0 Solving 15 + 19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + 19x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + 19x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 19x + x2 = 0 + -15 19x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 19x + x2 = -15 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 = -15 + 90.25 Reorder the terms: 90.25 + 19x + x2 = -15 + 90.25 Combine like terms: -15 + 90.25 = 75.25 90.25 + 19x + x2 = 75.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 75.25 Calculate the square root of the right side: 8.674675786 Break this problem into two subproblems by setting (x + 9.5) equal to 8.674675786 and -8.674675786.Subproblem 1
x + 9.5 = 8.674675786 Simplifying x + 9.5 = 8.674675786 Reorder the terms: 9.5 + x = 8.674675786 Solving 9.5 + x = 8.674675786 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 = 8.674675786 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 8.674675786 + -9.5 x = 8.674675786 + -9.5 Combine like terms: 8.674675786 + -9.5 = -0.825324214 x = -0.825324214 Simplifying x = -0.825324214Subproblem 2
x + 9.5 = -8.674675786 Simplifying x + 9.5 = -8.674675786 Reorder the terms: 9.5 + x = -8.674675786 Solving 9.5 + x = -8.674675786 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 = -8.674675786 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -8.674675786 + -9.5 x = -8.674675786 + -9.5 Combine like terms: -8.674675786 + -9.5 = -18.174675786 x = -18.174675786 Simplifying x = -18.174675786Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.825324214, -18.174675786}
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