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Simplifying 0.10x(x + 80) + 0.10x = 9 Reorder the terms: 0.10x(80 + x) + 0.10x = 9 (80 * 0.10x + x * 0.10x) + 0.10x = 9 (8x + 0.10x2) + 0.10x = 9 Reorder the terms: 8x + 0.10x + 0.10x2 = 9 Combine like terms: 8x + 0.10x = 8.1x 8.1x + 0.10x2 = 9 Solving 8.1x + 0.10x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + 8.1x + 0.10x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 8.1x + 0.10x2 = 0 Begin completing the square. Divide all terms by 0.10 the coefficient of the squared term: Divide each side by '0.10'. -90 + 81x + x2 = 0 Move the constant term to the right: Add '90' to each side of the equation. -90 + 81x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 81x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 81x + x2 = 0 + 90 81x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 81x + x2 = 90 The x term is 81x. Take half its coefficient (40.5). Square it (1640.25) and add it to both sides. Add '1640.25' to each side of the equation. 81x + 1640.25 + x2 = 90 + 1640.25 Reorder the terms: 1640.25 + 81x + x2 = 90 + 1640.25 Combine like terms: 90 + 1640.25 = 1730.25 1640.25 + 81x + x2 = 1730.25 Factor a perfect square on the left side: (x + 40.5)(x + 40.5) = 1730.25 Calculate the square root of the right side: 41.596273872 Break this problem into two subproblems by setting (x + 40.5) equal to 41.596273872 and -41.596273872.Subproblem 1
x + 40.5 = 41.596273872 Simplifying x + 40.5 = 41.596273872 Reorder the terms: 40.5 + x = 41.596273872 Solving 40.5 + x = 41.596273872 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40.5' to each side of the equation. 40.5 + -40.5 + x = 41.596273872 + -40.5 Combine like terms: 40.5 + -40.5 = 0.0 0.0 + x = 41.596273872 + -40.5 x = 41.596273872 + -40.5 Combine like terms: 41.596273872 + -40.5 = 1.096273872 x = 1.096273872 Simplifying x = 1.096273872Subproblem 2
x + 40.5 = -41.596273872 Simplifying x + 40.5 = -41.596273872 Reorder the terms: 40.5 + x = -41.596273872 Solving 40.5 + x = -41.596273872 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40.5' to each side of the equation. 40.5 + -40.5 + x = -41.596273872 + -40.5 Combine like terms: 40.5 + -40.5 = 0.0 0.0 + x = -41.596273872 + -40.5 x = -41.596273872 + -40.5 Combine like terms: -41.596273872 + -40.5 = -82.096273872 x = -82.096273872 Simplifying x = -82.096273872Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.096273872, -82.096273872}
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