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Simplifying 5x2 + 80x + 64 = 0 Reorder the terms: 64 + 80x + 5x2 = 0 Solving 64 + 80x + 5x2 = 0 Solving for variable 'x'. 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 = 51.2 64 + 16x + x2 = 51.2 Factor a perfect square on the left side: (x + 8)(x + 8) = 51.2 Calculate the square root of the right side: 7.155417528 Break this problem into two subproblems by setting (x + 8) equal to 7.155417528 and -7.155417528.Subproblem 1
x + 8 = 7.155417528 Simplifying x + 8 = 7.155417528 Reorder the terms: 8 + x = 7.155417528 Solving 8 + x = 7.155417528 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 = 7.155417528 + -8 Combine like terms: 8 + -8 = 0 0 + x = 7.155417528 + -8 x = 7.155417528 + -8 Combine like terms: 7.155417528 + -8 = -0.844582472 x = -0.844582472 Simplifying x = -0.844582472Subproblem 2
x + 8 = -7.155417528 Simplifying x + 8 = -7.155417528 Reorder the terms: 8 + x = -7.155417528 Solving 8 + x = -7.155417528 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 = -7.155417528 + -8 Combine like terms: 8 + -8 = 0 0 + x = -7.155417528 + -8 x = -7.155417528 + -8 Combine like terms: -7.155417528 + -8 = -15.155417528 x = -15.155417528 Simplifying x = -15.155417528Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.844582472, -15.155417528}
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