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Simplifying 5x2 + -9 = -20.5x Reorder the terms: -9 + 5x2 = -20.5x Solving -9 + 5x2 = -20.5x Solving for variable 'x'. Reorder the terms: -9 + 20.5x + 5x2 = -20.5x + 20.5x Combine like terms: -20.5x + 20.5x = 0.0 -9 + 20.5x + 5x2 = 0.0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.8 + 4.1x + x2 = 0.0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + 4.1x + 1.8 + x2 = 0.0 + 1.8 Reorder the terms: -1.8 + 1.8 + 4.1x + x2 = 0.0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + 4.1x + x2 = 0.0 + 1.8 4.1x + x2 = 0.0 + 1.8 Combine like terms: 0.0 + 1.8 = 1.8 4.1x + x2 = 1.8 The x term is 4.1x. Take half its coefficient (2.05). Square it (4.2025) and add it to both sides. Add '4.2025' to each side of the equation. 4.1x + 4.2025 + x2 = 1.8 + 4.2025 Reorder the terms: 4.2025 + 4.1x + x2 = 1.8 + 4.2025 Combine like terms: 1.8 + 4.2025 = 6.0025 4.2025 + 4.1x + x2 = 6.0025 Factor a perfect square on the left side: (x + 2.05)(x + 2.05) = 6.0025 Calculate the square root of the right side: 2.45 Break this problem into two subproblems by setting (x + 2.05) equal to 2.45 and -2.45.Subproblem 1
x + 2.05 = 2.45 Simplifying x + 2.05 = 2.45 Reorder the terms: 2.05 + x = 2.45 Solving 2.05 + x = 2.45 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.05' to each side of the equation. 2.05 + -2.05 + x = 2.45 + -2.05 Combine like terms: 2.05 + -2.05 = 0.00 0.00 + x = 2.45 + -2.05 x = 2.45 + -2.05 Combine like terms: 2.45 + -2.05 = 0.4 x = 0.4 Simplifying x = 0.4Subproblem 2
x + 2.05 = -2.45 Simplifying x + 2.05 = -2.45 Reorder the terms: 2.05 + x = -2.45 Solving 2.05 + x = -2.45 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.05' to each side of the equation. 2.05 + -2.05 + x = -2.45 + -2.05 Combine like terms: 2.05 + -2.05 = 0.00 0.00 + x = -2.45 + -2.05 x = -2.45 + -2.05 Combine like terms: -2.45 + -2.05 = -4.5 x = -4.5 Simplifying x = -4.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4, -4.5}
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