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Simplifying x2 + 98x + 64 = 0 Reorder the terms: 64 + 98x + x2 = 0 Solving 64 + 98x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-64' to each side of the equation. 64 + 98x + -64 + x2 = 0 + -64 Reorder the terms: 64 + -64 + 98x + x2 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + 98x + x2 = 0 + -64 98x + x2 = 0 + -64 Combine like terms: 0 + -64 = -64 98x + x2 = -64 The x term is 98x. Take half its coefficient (49). Square it (2401) and add it to both sides. Add '2401' to each side of the equation. 98x + 2401 + x2 = -64 + 2401 Reorder the terms: 2401 + 98x + x2 = -64 + 2401 Combine like terms: -64 + 2401 = 2337 2401 + 98x + x2 = 2337 Factor a perfect square on the left side: (x + 49)(x + 49) = 2337 Calculate the square root of the right side: 48.342527861 Break this problem into two subproblems by setting (x + 49) equal to 48.342527861 and -48.342527861.Subproblem 1
x + 49 = 48.342527861 Simplifying x + 49 = 48.342527861 Reorder the terms: 49 + x = 48.342527861 Solving 49 + x = 48.342527861 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-49' to each side of the equation. 49 + -49 + x = 48.342527861 + -49 Combine like terms: 49 + -49 = 0 0 + x = 48.342527861 + -49 x = 48.342527861 + -49 Combine like terms: 48.342527861 + -49 = -0.657472139 x = -0.657472139 Simplifying x = -0.657472139Subproblem 2
x + 49 = -48.342527861 Simplifying x + 49 = -48.342527861 Reorder the terms: 49 + x = -48.342527861 Solving 49 + x = -48.342527861 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-49' to each side of the equation. 49 + -49 + x = -48.342527861 + -49 Combine like terms: 49 + -49 = 0 0 + x = -48.342527861 + -49 x = -48.342527861 + -49 Combine like terms: -48.342527861 + -49 = -97.342527861 x = -97.342527861 Simplifying x = -97.342527861Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.657472139, -97.342527861}
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