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Simplifying x2 + 159x + -2100 = 0 Reorder the terms: -2100 + 159x + x2 = 0 Solving -2100 + 159x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2100' to each side of the equation. -2100 + 159x + 2100 + x2 = 0 + 2100 Reorder the terms: -2100 + 2100 + 159x + x2 = 0 + 2100 Combine like terms: -2100 + 2100 = 0 0 + 159x + x2 = 0 + 2100 159x + x2 = 0 + 2100 Combine like terms: 0 + 2100 = 2100 159x + x2 = 2100 The x term is 159x. Take half its coefficient (79.5). Square it (6320.25) and add it to both sides. Add '6320.25' to each side of the equation. 159x + 6320.25 + x2 = 2100 + 6320.25 Reorder the terms: 6320.25 + 159x + x2 = 2100 + 6320.25 Combine like terms: 2100 + 6320.25 = 8420.25 6320.25 + 159x + x2 = 8420.25 Factor a perfect square on the left side: (x + 79.5)(x + 79.5) = 8420.25 Calculate the square root of the right side: 91.761920207 Break this problem into two subproblems by setting (x + 79.5) equal to 91.761920207 and -91.761920207.Subproblem 1
x + 79.5 = 91.761920207 Simplifying x + 79.5 = 91.761920207 Reorder the terms: 79.5 + x = 91.761920207 Solving 79.5 + x = 91.761920207 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-79.5' to each side of the equation. 79.5 + -79.5 + x = 91.761920207 + -79.5 Combine like terms: 79.5 + -79.5 = 0.0 0.0 + x = 91.761920207 + -79.5 x = 91.761920207 + -79.5 Combine like terms: 91.761920207 + -79.5 = 12.261920207 x = 12.261920207 Simplifying x = 12.261920207Subproblem 2
x + 79.5 = -91.761920207 Simplifying x + 79.5 = -91.761920207 Reorder the terms: 79.5 + x = -91.761920207 Solving 79.5 + x = -91.761920207 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-79.5' to each side of the equation. 79.5 + -79.5 + x = -91.761920207 + -79.5 Combine like terms: 79.5 + -79.5 = 0.0 0.0 + x = -91.761920207 + -79.5 x = -91.761920207 + -79.5 Combine like terms: -91.761920207 + -79.5 = -171.261920207 x = -171.261920207 Simplifying x = -171.261920207Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.261920207, -171.261920207}
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