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Simplifying -5x2 + -80x = -64 Reorder the terms: -80x + -5x2 = -64 Solving -80x + -5x2 = -64 Solving for variable 'x'. Reorder the terms: 64 + -80x + -5x2 = -64 + 64 Combine like terms: -64 + 64 = 0 64 + -80x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -12.8 + 16x + x2 = 0 Move the constant term to the right: Add '12.8' to each side of the equation. -12.8 + 16x + 12.8 + x2 = 0 + 12.8 Reorder the terms: -12.8 + 12.8 + 16x + x2 = 0 + 12.8 Combine like terms: -12.8 + 12.8 = 0.0 0.0 + 16x + x2 = 0 + 12.8 16x + x2 = 0 + 12.8 Combine like terms: 0 + 12.8 = 12.8 16x + x2 = 12.8 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 12.8 + 64 Reorder the terms: 64 + 16x + x2 = 12.8 + 64 Combine like terms: 12.8 + 64 = 76.8 64 + 16x + x2 = 76.8 Factor a perfect square on the left side: (x + 8)(x + 8) = 76.8 Calculate the square root of the right side: 8.76356092 Break this problem into two subproblems by setting (x + 8) equal to 8.76356092 and -8.76356092.Subproblem 1
x + 8 = 8.76356092 Simplifying x + 8 = 8.76356092 Reorder the terms: 8 + x = 8.76356092 Solving 8 + x = 8.76356092 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 8.76356092 + -8 Combine like terms: 8 + -8 = 0 0 + x = 8.76356092 + -8 x = 8.76356092 + -8 Combine like terms: 8.76356092 + -8 = 0.76356092 x = 0.76356092 Simplifying x = 0.76356092Subproblem 2
x + 8 = -8.76356092 Simplifying x + 8 = -8.76356092 Reorder the terms: 8 + x = -8.76356092 Solving 8 + x = -8.76356092 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -8.76356092 + -8 Combine like terms: 8 + -8 = 0 0 + x = -8.76356092 + -8 x = -8.76356092 + -8 Combine like terms: -8.76356092 + -8 = -16.76356092 x = -16.76356092 Simplifying x = -16.76356092Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.76356092, -16.76356092}
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