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Simplifying 10x2 + 9x + -108 = 0 Reorder the terms: -108 + 9x + 10x2 = 0 Solving -108 + 9x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -10.8 + 0.9x + x2 = 0 Move the constant term to the right: Add '10.8' to each side of the equation. -10.8 + 0.9x + 10.8 + x2 = 0 + 10.8 Reorder the terms: -10.8 + 10.8 + 0.9x + x2 = 0 + 10.8 Combine like terms: -10.8 + 10.8 = 0.0 0.0 + 0.9x + x2 = 0 + 10.8 0.9x + x2 = 0 + 10.8 Combine like terms: 0 + 10.8 = 10.8 0.9x + x2 = 10.8 The x term is 0.9x. Take half its coefficient (0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. 0.9x + 0.2025 + x2 = 10.8 + 0.2025 Reorder the terms: 0.2025 + 0.9x + x2 = 10.8 + 0.2025 Combine like terms: 10.8 + 0.2025 = 11.0025 0.2025 + 0.9x + x2 = 11.0025 Factor a perfect square on the left side: (x + 0.45)(x + 0.45) = 11.0025 Calculate the square root of the right side: 3.317001658 Break this problem into two subproblems by setting (x + 0.45) equal to 3.317001658 and -3.317001658.Subproblem 1
x + 0.45 = 3.317001658 Simplifying x + 0.45 = 3.317001658 Reorder the terms: 0.45 + x = 3.317001658 Solving 0.45 + x = 3.317001658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + x = 3.317001658 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + x = 3.317001658 + -0.45 x = 3.317001658 + -0.45 Combine like terms: 3.317001658 + -0.45 = 2.867001658 x = 2.867001658 Simplifying x = 2.867001658Subproblem 2
x + 0.45 = -3.317001658 Simplifying x + 0.45 = -3.317001658 Reorder the terms: 0.45 + x = -3.317001658 Solving 0.45 + x = -3.317001658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + x = -3.317001658 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + x = -3.317001658 + -0.45 x = -3.317001658 + -0.45 Combine like terms: -3.317001658 + -0.45 = -3.767001658 x = -3.767001658 Simplifying x = -3.767001658Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.867001658, -3.767001658}
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