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Simplifying 10x2 = -9x + 5 Reorder the terms: 10x2 = 5 + -9x Solving 10x2 = 5 + -9x Solving for variable 'x'. Reorder the terms: -5 + 9x + 10x2 = 5 + -9x + -5 + 9x Reorder the terms: -5 + 9x + 10x2 = 5 + -5 + -9x + 9x Combine like terms: 5 + -5 = 0 -5 + 9x + 10x2 = 0 + -9x + 9x -5 + 9x + 10x2 = -9x + 9x Combine like terms: -9x + 9x = 0 -5 + 9x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.5 + 0.9x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 0.9x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 0.9x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.9x + x2 = 0 + 0.5 0.9x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 0.9x + x2 = 0.5 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 = 0.5 + 0.2025 Reorder the terms: 0.2025 + 0.9x + x2 = 0.5 + 0.2025 Combine like terms: 0.5 + 0.2025 = 0.7025 0.2025 + 0.9x + x2 = 0.7025 Factor a perfect square on the left side: (x + 0.45)(x + 0.45) = 0.7025 Calculate the square root of the right side: 0.838152731 Break this problem into two subproblems by setting (x + 0.45) equal to 0.838152731 and -0.838152731.Subproblem 1
x + 0.45 = 0.838152731 Simplifying x + 0.45 = 0.838152731 Reorder the terms: 0.45 + x = 0.838152731 Solving 0.45 + x = 0.838152731 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 = 0.838152731 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + x = 0.838152731 + -0.45 x = 0.838152731 + -0.45 Combine like terms: 0.838152731 + -0.45 = 0.388152731 x = 0.388152731 Simplifying x = 0.388152731Subproblem 2
x + 0.45 = -0.838152731 Simplifying x + 0.45 = -0.838152731 Reorder the terms: 0.45 + x = -0.838152731 Solving 0.45 + x = -0.838152731 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 = -0.838152731 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + x = -0.838152731 + -0.45 x = -0.838152731 + -0.45 Combine like terms: -0.838152731 + -0.45 = -1.288152731 x = -1.288152731 Simplifying x = -1.288152731Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.388152731, -1.288152731}
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