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Simplifying x2 + 20x + -100 = x Reorder the terms: -100 + 20x + x2 = x Solving -100 + 20x + x2 = x Solving for variable 'x'. Reorder the terms: -100 + 20x + -1x + x2 = x + -1x Combine like terms: 20x + -1x = 19x -100 + 19x + x2 = x + -1x Combine like terms: x + -1x = 0 -100 + 19x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 19x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 19x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 19x + x2 = 0 + 100 19x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 19x + x2 = 100 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 = 100 + 90.25 Reorder the terms: 90.25 + 19x + x2 = 100 + 90.25 Combine like terms: 100 + 90.25 = 190.25 90.25 + 19x + x2 = 190.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 190.25 Calculate the square root of the right side: 13.793114224 Break this problem into two subproblems by setting (x + 9.5) equal to 13.793114224 and -13.793114224.Subproblem 1
x + 9.5 = 13.793114224 Simplifying x + 9.5 = 13.793114224 Reorder the terms: 9.5 + x = 13.793114224 Solving 9.5 + x = 13.793114224 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 = 13.793114224 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 13.793114224 + -9.5 x = 13.793114224 + -9.5 Combine like terms: 13.793114224 + -9.5 = 4.293114224 x = 4.293114224 Simplifying x = 4.293114224Subproblem 2
x + 9.5 = -13.793114224 Simplifying x + 9.5 = -13.793114224 Reorder the terms: 9.5 + x = -13.793114224 Solving 9.5 + x = -13.793114224 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 = -13.793114224 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -13.793114224 + -9.5 x = -13.793114224 + -9.5 Combine like terms: -13.793114224 + -9.5 = -23.293114224 x = -23.293114224 Simplifying x = -23.293114224Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.293114224, -23.293114224}
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