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Simplifying x2 + 19x + -72 = 0 Reorder the terms: -72 + 19x + x2 = 0 Solving -72 + 19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + 19x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + 19x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 19x + x2 = 0 + 72 19x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 19x + x2 = 72 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 = 72 + 90.25 Reorder the terms: 90.25 + 19x + x2 = 72 + 90.25 Combine like terms: 72 + 90.25 = 162.25 90.25 + 19x + x2 = 162.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 162.25 Calculate the square root of the right side: 12.737739203 Break this problem into two subproblems by setting (x + 9.5) equal to 12.737739203 and -12.737739203.Subproblem 1
x + 9.5 = 12.737739203 Simplifying x + 9.5 = 12.737739203 Reorder the terms: 9.5 + x = 12.737739203 Solving 9.5 + x = 12.737739203 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 = 12.737739203 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 12.737739203 + -9.5 x = 12.737739203 + -9.5 Combine like terms: 12.737739203 + -9.5 = 3.237739203 x = 3.237739203 Simplifying x = 3.237739203Subproblem 2
x + 9.5 = -12.737739203 Simplifying x + 9.5 = -12.737739203 Reorder the terms: 9.5 + x = -12.737739203 Solving 9.5 + x = -12.737739203 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 = -12.737739203 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -12.737739203 + -9.5 x = -12.737739203 + -9.5 Combine like terms: -12.737739203 + -9.5 = -22.237739203 x = -22.237739203 Simplifying x = -22.237739203Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.237739203, -22.237739203}
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