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Simplifying 0.5(x + 10) * 1.1x = 69 Reorder the terms: 0.5(10 + x) * 1.1x = 69 Reorder the terms for easier multiplication: 0.5 * 1.1x(10 + x) = 69 Multiply 0.5 * 1.1 0.55x(10 + x) = 69 (10 * 0.55x + x * 0.55x) = 69 (5.5x + 0.55x2) = 69 Solving 5.5x + 0.55x2 = 69 Solving for variable 'x'. Reorder the terms: -69 + 5.5x + 0.55x2 = 69 + -69 Combine like terms: 69 + -69 = 0 -69 + 5.5x + 0.55x2 = 0 Begin completing the square. Divide all terms by 0.55 the coefficient of the squared term: Divide each side by '0.55'. -125.4545455 + 10x + x2 = 0 Move the constant term to the right: Add '125.4545455' to each side of the equation. -125.4545455 + 10x + 125.4545455 + x2 = 0 + 125.4545455 Reorder the terms: -125.4545455 + 125.4545455 + 10x + x2 = 0 + 125.4545455 Combine like terms: -125.4545455 + 125.4545455 = 0.0000000 0.0000000 + 10x + x2 = 0 + 125.4545455 10x + x2 = 0 + 125.4545455 Combine like terms: 0 + 125.4545455 = 125.4545455 10x + x2 = 125.4545455 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 125.4545455 + 25 Reorder the terms: 25 + 10x + x2 = 125.4545455 + 25 Combine like terms: 125.4545455 + 25 = 150.4545455 25 + 10x + x2 = 150.4545455 Factor a perfect square on the left side: (x + 5)(x + 5) = 150.4545455 Calculate the square root of the right side: 12.265991419 Break this problem into two subproblems by setting (x + 5) equal to 12.265991419 and -12.265991419.Subproblem 1
x + 5 = 12.265991419 Simplifying x + 5 = 12.265991419 Reorder the terms: 5 + x = 12.265991419 Solving 5 + x = 12.265991419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 12.265991419 + -5 Combine like terms: 5 + -5 = 0 0 + x = 12.265991419 + -5 x = 12.265991419 + -5 Combine like terms: 12.265991419 + -5 = 7.265991419 x = 7.265991419 Simplifying x = 7.265991419Subproblem 2
x + 5 = -12.265991419 Simplifying x + 5 = -12.265991419 Reorder the terms: 5 + x = -12.265991419 Solving 5 + x = -12.265991419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -12.265991419 + -5 Combine like terms: 5 + -5 = 0 0 + x = -12.265991419 + -5 x = -12.265991419 + -5 Combine like terms: -12.265991419 + -5 = -17.265991419 x = -17.265991419 Simplifying x = -17.265991419Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.265991419, -17.265991419}
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