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Simplifying x2 + -19x + 30 = 0 Reorder the terms: 30 + -19x + x2 = 0 Solving 30 + -19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + -19x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + -19x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -19x + x2 = 0 + -30 -19x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 -19x + x2 = -30 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 = -30 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -30 + 90.25 Combine like terms: -30 + 90.25 = 60.25 90.25 + -19x + x2 = 60.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (x + -9.5) equal to 7.762087348 and -7.762087348.Subproblem 1
x + -9.5 = 7.762087348 Simplifying x + -9.5 = 7.762087348 Reorder the terms: -9.5 + x = 7.762087348 Solving -9.5 + x = 7.762087348 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 = 7.762087348 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 7.762087348 + 9.5 x = 7.762087348 + 9.5 Combine like terms: 7.762087348 + 9.5 = 17.262087348 x = 17.262087348 Simplifying x = 17.262087348Subproblem 2
x + -9.5 = -7.762087348 Simplifying x + -9.5 = -7.762087348 Reorder the terms: -9.5 + x = -7.762087348 Solving -9.5 + x = -7.762087348 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 = -7.762087348 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -7.762087348 + 9.5 x = -7.762087348 + 9.5 Combine like terms: -7.762087348 + 9.5 = 1.737912652 x = 1.737912652 Simplifying x = 1.737912652Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.262087348, 1.737912652}
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