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Simplifying 5.1 + -5.1x = x2 Solving 5.1 + -5.1x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 5.1 + -5.1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5.1 + 5.1x + x2 = 0 Move the constant term to the right: Add '5.1' to each side of the equation. -5.1 + 5.1x + 5.1 + x2 = 0 + 5.1 Reorder the terms: -5.1 + 5.1 + 5.1x + x2 = 0 + 5.1 Combine like terms: -5.1 + 5.1 = 0.0 0.0 + 5.1x + x2 = 0 + 5.1 5.1x + x2 = 0 + 5.1 Combine like terms: 0 + 5.1 = 5.1 5.1x + x2 = 5.1 The x term is 5.1x. Take half its coefficient (2.55). Square it (6.5025) and add it to both sides. Add '6.5025' to each side of the equation. 5.1x + 6.5025 + x2 = 5.1 + 6.5025 Reorder the terms: 6.5025 + 5.1x + x2 = 5.1 + 6.5025 Combine like terms: 5.1 + 6.5025 = 11.6025 6.5025 + 5.1x + x2 = 11.6025 Factor a perfect square on the left side: (x + 2.55)(x + 2.55) = 11.6025 Calculate the square root of the right side: 3.406244266 Break this problem into two subproblems by setting (x + 2.55) equal to 3.406244266 and -3.406244266.Subproblem 1
x + 2.55 = 3.406244266 Simplifying x + 2.55 = 3.406244266 Reorder the terms: 2.55 + x = 3.406244266 Solving 2.55 + x = 3.406244266 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.55' to each side of the equation. 2.55 + -2.55 + x = 3.406244266 + -2.55 Combine like terms: 2.55 + -2.55 = 0.00 0.00 + x = 3.406244266 + -2.55 x = 3.406244266 + -2.55 Combine like terms: 3.406244266 + -2.55 = 0.856244266 x = 0.856244266 Simplifying x = 0.856244266Subproblem 2
x + 2.55 = -3.406244266 Simplifying x + 2.55 = -3.406244266 Reorder the terms: 2.55 + x = -3.406244266 Solving 2.55 + x = -3.406244266 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.55' to each side of the equation. 2.55 + -2.55 + x = -3.406244266 + -2.55 Combine like terms: 2.55 + -2.55 = 0.00 0.00 + x = -3.406244266 + -2.55 x = -3.406244266 + -2.55 Combine like terms: -3.406244266 + -2.55 = -5.956244266 x = -5.956244266 Simplifying x = -5.956244266Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.856244266, -5.956244266}
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