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Simplifying 10x2 = 9x + 2 Reorder the terms: 10x2 = 2 + 9x Solving 10x2 = 2 + 9x Solving for variable 'x'. Reorder the terms: -2 + -9x + 10x2 = 2 + 9x + -2 + -9x Reorder the terms: -2 + -9x + 10x2 = 2 + -2 + 9x + -9x Combine like terms: 2 + -2 = 0 -2 + -9x + 10x2 = 0 + 9x + -9x -2 + -9x + 10x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -2 + -9x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.2 + -0.9x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -0.9x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -0.9x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -0.9x + x2 = 0 + 0.2 -0.9x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -0.9x + x2 = 0.2 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 = 0.2 + 0.2025 Reorder the terms: 0.2025 + -0.9x + x2 = 0.2 + 0.2025 Combine like terms: 0.2 + 0.2025 = 0.4025 0.2025 + -0.9x + x2 = 0.4025 Factor a perfect square on the left side: (x + -0.45)(x + -0.45) = 0.4025 Calculate the square root of the right side: 0.634428877 Break this problem into two subproblems by setting (x + -0.45) equal to 0.634428877 and -0.634428877.Subproblem 1
x + -0.45 = 0.634428877 Simplifying x + -0.45 = 0.634428877 Reorder the terms: -0.45 + x = 0.634428877 Solving -0.45 + x = 0.634428877 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 = 0.634428877 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x = 0.634428877 + 0.45 x = 0.634428877 + 0.45 Combine like terms: 0.634428877 + 0.45 = 1.084428877 x = 1.084428877 Simplifying x = 1.084428877Subproblem 2
x + -0.45 = -0.634428877 Simplifying x + -0.45 = -0.634428877 Reorder the terms: -0.45 + x = -0.634428877 Solving -0.45 + x = -0.634428877 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 = -0.634428877 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x = -0.634428877 + 0.45 x = -0.634428877 + 0.45 Combine like terms: -0.634428877 + 0.45 = -0.184428877 x = -0.184428877 Simplifying x = -0.184428877Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.084428877, -0.184428877}
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