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Simplifying 4.9x2 = 2 + 24.5x Solving 4.9x2 = 2 + 24.5x Solving for variable 'x'. Reorder the terms: -2 + -24.5x + 4.9x2 = 2 + 24.5x + -2 + -24.5x Reorder the terms: -2 + -24.5x + 4.9x2 = 2 + -2 + 24.5x + -24.5x Combine like terms: 2 + -2 = 0 -2 + -24.5x + 4.9x2 = 0 + 24.5x + -24.5x -2 + -24.5x + 4.9x2 = 24.5x + -24.5x Combine like terms: 24.5x + -24.5x = 0.0 -2 + -24.5x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -0.4081632653 + -5x + x2 = 0 Move the constant term to the right: Add '0.4081632653' to each side of the equation. -0.4081632653 + -5x + 0.4081632653 + x2 = 0 + 0.4081632653 Reorder the terms: -0.4081632653 + 0.4081632653 + -5x + x2 = 0 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + -5x + x2 = 0 + 0.4081632653 -5x + x2 = 0 + 0.4081632653 Combine like terms: 0 + 0.4081632653 = 0.4081632653 -5x + x2 = 0.4081632653 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 = 0.4081632653 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 0.4081632653 + 6.25 Combine like terms: 0.4081632653 + 6.25 = 6.6581632653 6.25 + -5x + x2 = 6.6581632653 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 6.6581632653 Calculate the square root of the right side: 2.580341695 Break this problem into two subproblems by setting (x + -2.5) equal to 2.580341695 and -2.580341695.Subproblem 1
x + -2.5 = 2.580341695 Simplifying x + -2.5 = 2.580341695 Reorder the terms: -2.5 + x = 2.580341695 Solving -2.5 + x = 2.580341695 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 = 2.580341695 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.580341695 + 2.5 x = 2.580341695 + 2.5 Combine like terms: 2.580341695 + 2.5 = 5.080341695 x = 5.080341695 Simplifying x = 5.080341695Subproblem 2
x + -2.5 = -2.580341695 Simplifying x + -2.5 = -2.580341695 Reorder the terms: -2.5 + x = -2.580341695 Solving -2.5 + x = -2.580341695 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 = -2.580341695 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.580341695 + 2.5 x = -2.580341695 + 2.5 Combine like terms: -2.580341695 + 2.5 = -0.080341695 x = -0.080341695 Simplifying x = -0.080341695Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.080341695, -0.080341695}
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