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Simplifying 5x(x + 1.1) = 18.5 Reorder the terms: 5x(1.1 + x) = 18.5 (1.1 * 5x + x * 5x) = 18.5 (5.5x + 5x2) = 18.5 Solving 5.5x + 5x2 = 18.5 Solving for variable 'x'. Reorder the terms: -18.5 + 5.5x + 5x2 = 18.5 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 -18.5 + 5.5x + 5x2 = 0.0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.7 + 1.1x + x2 = 0.0 Move the constant term to the right: Add '3.7' to each side of the equation. -3.7 + 1.1x + 3.7 + x2 = 0.0 + 3.7 Reorder the terms: -3.7 + 3.7 + 1.1x + x2 = 0.0 + 3.7 Combine like terms: -3.7 + 3.7 = 0.0 0.0 + 1.1x + x2 = 0.0 + 3.7 1.1x + x2 = 0.0 + 3.7 Combine like terms: 0.0 + 3.7 = 3.7 1.1x + x2 = 3.7 The x term is 1.1x. Take half its coefficient (0.55). Square it (0.3025) and add it to both sides. Add '0.3025' to each side of the equation. 1.1x + 0.3025 + x2 = 3.7 + 0.3025 Reorder the terms: 0.3025 + 1.1x + x2 = 3.7 + 0.3025 Combine like terms: 3.7 + 0.3025 = 4.0025 0.3025 + 1.1x + x2 = 4.0025 Factor a perfect square on the left side: (x + 0.55)(x + 0.55) = 4.0025 Calculate the square root of the right side: 2.000624902 Break this problem into two subproblems by setting (x + 0.55) equal to 2.000624902 and -2.000624902.Subproblem 1
x + 0.55 = 2.000624902 Simplifying x + 0.55 = 2.000624902 Reorder the terms: 0.55 + x = 2.000624902 Solving 0.55 + x = 2.000624902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.55' to each side of the equation. 0.55 + -0.55 + x = 2.000624902 + -0.55 Combine like terms: 0.55 + -0.55 = 0.00 0.00 + x = 2.000624902 + -0.55 x = 2.000624902 + -0.55 Combine like terms: 2.000624902 + -0.55 = 1.450624902 x = 1.450624902 Simplifying x = 1.450624902Subproblem 2
x + 0.55 = -2.000624902 Simplifying x + 0.55 = -2.000624902 Reorder the terms: 0.55 + x = -2.000624902 Solving 0.55 + x = -2.000624902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.55' to each side of the equation. 0.55 + -0.55 + x = -2.000624902 + -0.55 Combine like terms: 0.55 + -0.55 = 0.00 0.00 + x = -2.000624902 + -0.55 x = -2.000624902 + -0.55 Combine like terms: -2.000624902 + -0.55 = -2.550624902 x = -2.550624902 Simplifying x = -2.550624902Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.450624902, -2.550624902}
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