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Simplifying x2 + 19x + 32 = 0 Reorder the terms: 32 + 19x + x2 = 0 Solving 32 + 19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + 19x + -32 + x2 = 0 + -32 Reorder the terms: 32 + -32 + 19x + x2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + 19x + x2 = 0 + -32 19x + x2 = 0 + -32 Combine like terms: 0 + -32 = -32 19x + x2 = -32 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 = -32 + 90.25 Reorder the terms: 90.25 + 19x + x2 = -32 + 90.25 Combine like terms: -32 + 90.25 = 58.25 90.25 + 19x + x2 = 58.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 58.25 Calculate the square root of the right side: 7.632168761 Break this problem into two subproblems by setting (x + 9.5) equal to 7.632168761 and -7.632168761.Subproblem 1
x + 9.5 = 7.632168761 Simplifying x + 9.5 = 7.632168761 Reorder the terms: 9.5 + x = 7.632168761 Solving 9.5 + x = 7.632168761 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 = 7.632168761 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 7.632168761 + -9.5 x = 7.632168761 + -9.5 Combine like terms: 7.632168761 + -9.5 = -1.867831239 x = -1.867831239 Simplifying x = -1.867831239Subproblem 2
x + 9.5 = -7.632168761 Simplifying x + 9.5 = -7.632168761 Reorder the terms: 9.5 + x = -7.632168761 Solving 9.5 + x = -7.632168761 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 = -7.632168761 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -7.632168761 + -9.5 x = -7.632168761 + -9.5 Combine like terms: -7.632168761 + -9.5 = -17.132168761 x = -17.132168761 Simplifying x = -17.132168761Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.867831239, -17.132168761}
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