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Simplifying x2 + 30x + 98 = 0 Reorder the terms: 98 + 30x + x2 = 0 Solving 98 + 30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-98' to each side of the equation. 98 + 30x + -98 + x2 = 0 + -98 Reorder the terms: 98 + -98 + 30x + x2 = 0 + -98 Combine like terms: 98 + -98 = 0 0 + 30x + x2 = 0 + -98 30x + x2 = 0 + -98 Combine like terms: 0 + -98 = -98 30x + x2 = -98 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = -98 + 225 Reorder the terms: 225 + 30x + x2 = -98 + 225 Combine like terms: -98 + 225 = 127 225 + 30x + x2 = 127 Factor a perfect square on the left side: (x + 15)(x + 15) = 127 Calculate the square root of the right side: 11.26942767 Break this problem into two subproblems by setting (x + 15) equal to 11.26942767 and -11.26942767.Subproblem 1
x + 15 = 11.26942767 Simplifying x + 15 = 11.26942767 Reorder the terms: 15 + x = 11.26942767 Solving 15 + x = 11.26942767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 11.26942767 + -15 Combine like terms: 15 + -15 = 0 0 + x = 11.26942767 + -15 x = 11.26942767 + -15 Combine like terms: 11.26942767 + -15 = -3.73057233 x = -3.73057233 Simplifying x = -3.73057233Subproblem 2
x + 15 = -11.26942767 Simplifying x + 15 = -11.26942767 Reorder the terms: 15 + x = -11.26942767 Solving 15 + x = -11.26942767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -11.26942767 + -15 Combine like terms: 15 + -15 = 0 0 + x = -11.26942767 + -15 x = -11.26942767 + -15 Combine like terms: -11.26942767 + -15 = -26.26942767 x = -26.26942767 Simplifying x = -26.26942767Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.73057233, -26.26942767}
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