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Simplifying 5x2 = 9 + -5x Solving 5x2 = 9 + -5x Solving for variable 'x'. Reorder the terms: -9 + 5x + 5x2 = 9 + -5x + -9 + 5x Reorder the terms: -9 + 5x + 5x2 = 9 + -9 + -5x + 5x Combine like terms: 9 + -9 = 0 -9 + 5x + 5x2 = 0 + -5x + 5x -9 + 5x + 5x2 = -5x + 5x Combine like terms: -5x + 5x = 0 -9 + 5x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.8 + x + x2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + x + 1.8 + x2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + x + x2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x + x2 = 0 + 1.8 x + x2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 x + x2 = 1.8 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 1.8 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 1.8 + 0.25 Combine like terms: 1.8 + 0.25 = 2.05 1.25 + x2 = 2.05 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.05 Calculate the square root of the right side: 1.431782106 Break this problem into two subproblems by setting (x + 0.5) equal to 1.431782106 and -1.431782106.Subproblem 1
x + 0.5 = 1.431782106 Simplifying x + 0.5 = 1.431782106 Reorder the terms: 0.5 + x = 1.431782106 Solving 0.5 + x = 1.431782106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.431782106 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.431782106 + -0.5 x = 1.431782106 + -0.5 Combine like terms: 1.431782106 + -0.5 = 0.931782106 x = 0.931782106 Simplifying x = 0.931782106Subproblem 2
x + 0.5 = -1.431782106 Simplifying x + 0.5 = -1.431782106 Reorder the terms: 0.5 + x = -1.431782106 Solving 0.5 + x = -1.431782106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.431782106 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.431782106 + -0.5 x = -1.431782106 + -0.5 Combine like terms: -1.431782106 + -0.5 = -1.931782106 x = -1.931782106 Simplifying x = -1.931782106Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.931782106, -1.931782106}
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