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Simplifying -4.9x2 + 24.5x + 1 = 0 Reorder the terms: 1 + 24.5x + -4.9x2 = 0 Solving 1 + 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'. -0.2040816327 + -5x + x2 = 0 Move the constant term to the right: Add '0.2040816327' to each side of the equation. -0.2040816327 + -5x + 0.2040816327 + x2 = 0 + 0.2040816327 Reorder the terms: -0.2040816327 + 0.2040816327 + -5x + x2 = 0 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + -5x + x2 = 0 + 0.2040816327 -5x + x2 = 0 + 0.2040816327 Combine like terms: 0 + 0.2040816327 = 0.2040816327 -5x + x2 = 0.2040816327 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 = 0.2040816327 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 0.2040816327 + 6.25 Combine like terms: 0.2040816327 + 6.25 = 6.4540816327 6.25 + -5x + x2 = 6.4540816327 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 6.4540816327 Calculate the square root of the right side: 2.540488463 Break this problem into two subproblems by setting (x + -2.5) equal to 2.540488463 and -2.540488463.Subproblem 1
x + -2.5 = 2.540488463 Simplifying x + -2.5 = 2.540488463 Reorder the terms: -2.5 + x = 2.540488463 Solving -2.5 + x = 2.540488463 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 = 2.540488463 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.540488463 + 2.5 x = 2.540488463 + 2.5 Combine like terms: 2.540488463 + 2.5 = 5.040488463 x = 5.040488463 Simplifying x = 5.040488463Subproblem 2
x + -2.5 = -2.540488463 Simplifying x + -2.5 = -2.540488463 Reorder the terms: -2.5 + x = -2.540488463 Solving -2.5 + x = -2.540488463 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 = -2.540488463 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.540488463 + 2.5 x = -2.540488463 + 2.5 Combine like terms: -2.540488463 + 2.5 = -0.040488463 x = -0.040488463 Simplifying x = -0.040488463Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.040488463, -0.040488463}
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