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Simplifying -4.9x2 + 24.5x + 8.6 = 0 Reorder the terms: 8.6 + 24.5x + -4.9x2 = 0 Solving 8.6 + 24.5x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -1.755102041 + -5x + x2 = 0 Move the constant term to the right: Add '1.755102041' to each side of the equation. -1.755102041 + -5x + 1.755102041 + x2 = 0 + 1.755102041 Reorder the terms: -1.755102041 + 1.755102041 + -5x + x2 = 0 + 1.755102041 Combine like terms: -1.755102041 + 1.755102041 = 0.000000000 0.000000000 + -5x + x2 = 0 + 1.755102041 -5x + x2 = 0 + 1.755102041 Combine like terms: 0 + 1.755102041 = 1.755102041 -5x + x2 = 1.755102041 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 1.755102041 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 1.755102041 + 6.25 Combine like terms: 1.755102041 + 6.25 = 8.005102041 6.25 + -5x + x2 = 8.005102041 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 8.005102041 Calculate the square root of the right side: 2.829328903 Break this problem into two subproblems by setting (x + -2.5) equal to 2.829328903 and -2.829328903.Subproblem 1
x + -2.5 = 2.829328903 Simplifying x + -2.5 = 2.829328903 Reorder the terms: -2.5 + x = 2.829328903 Solving -2.5 + x = 2.829328903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.829328903 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.829328903 + 2.5 x = 2.829328903 + 2.5 Combine like terms: 2.829328903 + 2.5 = 5.329328903 x = 5.329328903 Simplifying x = 5.329328903Subproblem 2
x + -2.5 = -2.829328903 Simplifying x + -2.5 = -2.829328903 Reorder the terms: -2.5 + x = -2.829328903 Solving -2.5 + x = -2.829328903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.829328903 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.829328903 + 2.5 x = -2.829328903 + 2.5 Combine like terms: -2.829328903 + 2.5 = -0.329328903 x = -0.329328903 Simplifying x = -0.329328903Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.329328903, -0.329328903}
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