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Simplifying x2 + 19x + -10077696 = 0 Reorder the terms: -10077696 + 19x + x2 = 0 Solving -10077696 + 19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '10077696' to each side of the equation. -10077696 + 19x + 10077696 + x2 = 0 + 10077696 Reorder the terms: -10077696 + 10077696 + 19x + x2 = 0 + 10077696 Combine like terms: -10077696 + 10077696 = 0 0 + 19x + x2 = 0 + 10077696 19x + x2 = 0 + 10077696 Combine like terms: 0 + 10077696 = 10077696 19x + x2 = 10077696 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 = 10077696 + 90.25 Reorder the terms: 90.25 + 19x + x2 = 10077696 + 90.25 Combine like terms: 10077696 + 90.25 = 10077786.25 90.25 + 19x + x2 = 10077786.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 10077786.25 Calculate the square root of the right side: 3174.552921279 Break this problem into two subproblems by setting (x + 9.5) equal to 3174.552921279 and -3174.552921279.Subproblem 1
x + 9.5 = 3174.552921279 Simplifying x + 9.5 = 3174.552921279 Reorder the terms: 9.5 + x = 3174.552921279 Solving 9.5 + x = 3174.552921279 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 = 3174.552921279 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 3174.552921279 + -9.5 x = 3174.552921279 + -9.5 Combine like terms: 3174.552921279 + -9.5 = 3165.052921279 x = 3165.052921279 Simplifying x = 3165.052921279Subproblem 2
x + 9.5 = -3174.552921279 Simplifying x + 9.5 = -3174.552921279 Reorder the terms: 9.5 + x = -3174.552921279 Solving 9.5 + x = -3174.552921279 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 = -3174.552921279 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -3174.552921279 + -9.5 x = -3174.552921279 + -9.5 Combine like terms: -3174.552921279 + -9.5 = -3184.052921279 x = -3184.052921279 Simplifying x = -3184.052921279Solution
The solution to the problem is based on the solutions from the subproblems. x = {3165.052921279, -3184.052921279}
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