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Simplifying x2 + 80x + 96 = 0 Reorder the terms: 96 + 80x + x2 = 0 Solving 96 + 80x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-96' to each side of the equation. 96 + 80x + -96 + x2 = 0 + -96 Reorder the terms: 96 + -96 + 80x + x2 = 0 + -96 Combine like terms: 96 + -96 = 0 0 + 80x + x2 = 0 + -96 80x + x2 = 0 + -96 Combine like terms: 0 + -96 = -96 80x + x2 = -96 The x term is 80x. Take half its coefficient (40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. 80x + 1600 + x2 = -96 + 1600 Reorder the terms: 1600 + 80x + x2 = -96 + 1600 Combine like terms: -96 + 1600 = 1504 1600 + 80x + x2 = 1504 Factor a perfect square on the left side: (x + 40)(x + 40) = 1504 Calculate the square root of the right side: 38.781438859 Break this problem into two subproblems by setting (x + 40) equal to 38.781438859 and -38.781438859.Subproblem 1
x + 40 = 38.781438859 Simplifying x + 40 = 38.781438859 Reorder the terms: 40 + x = 38.781438859 Solving 40 + x = 38.781438859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = 38.781438859 + -40 Combine like terms: 40 + -40 = 0 0 + x = 38.781438859 + -40 x = 38.781438859 + -40 Combine like terms: 38.781438859 + -40 = -1.218561141 x = -1.218561141 Simplifying x = -1.218561141Subproblem 2
x + 40 = -38.781438859 Simplifying x + 40 = -38.781438859 Reorder the terms: 40 + x = -38.781438859 Solving 40 + x = -38.781438859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = -38.781438859 + -40 Combine like terms: 40 + -40 = 0 0 + x = -38.781438859 + -40 x = -38.781438859 + -40 Combine like terms: -38.781438859 + -40 = -78.781438859 x = -78.781438859 Simplifying x = -78.781438859Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.218561141, -78.781438859}
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