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Simplifying 10x2 + 9x = 50 Reorder the terms: 9x + 10x2 = 50 Solving 9x + 10x2 = 50 Solving for variable 'x'. Reorder the terms: -50 + 9x + 10x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + 9x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -5 + 0.9x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 0.9x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 0.9x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 0.9x + x2 = 0 + 5 0.9x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 0.9x + x2 = 5 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 = 5 + 0.2025 Reorder the terms: 0.2025 + 0.9x + x2 = 5 + 0.2025 Combine like terms: 5 + 0.2025 = 5.2025 0.2025 + 0.9x + x2 = 5.2025 Factor a perfect square on the left side: (x + 0.45)(x + 0.45) = 5.2025 Calculate the square root of the right side: 2.280898946 Break this problem into two subproblems by setting (x + 0.45) equal to 2.280898946 and -2.280898946.Subproblem 1
x + 0.45 = 2.280898946 Simplifying x + 0.45 = 2.280898946 Reorder the terms: 0.45 + x = 2.280898946 Solving 0.45 + x = 2.280898946 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 = 2.280898946 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + x = 2.280898946 + -0.45 x = 2.280898946 + -0.45 Combine like terms: 2.280898946 + -0.45 = 1.830898946 x = 1.830898946 Simplifying x = 1.830898946Subproblem 2
x + 0.45 = -2.280898946 Simplifying x + 0.45 = -2.280898946 Reorder the terms: 0.45 + x = -2.280898946 Solving 0.45 + x = -2.280898946 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 = -2.280898946 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + x = -2.280898946 + -0.45 x = -2.280898946 + -0.45 Combine like terms: -2.280898946 + -0.45 = -2.730898946 x = -2.730898946 Simplifying x = -2.730898946Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.830898946, -2.730898946}
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