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Simplifying -4.9x2 + 24.5x + 9.5 = 0 Reorder the terms: 9.5 + 24.5x + -4.9x2 = 0 Solving 9.5 + 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'. -1.93877551 + -5x + x2 = 0 Move the constant term to the right: Add '1.93877551' to each side of the equation. -1.93877551 + -5x + 1.93877551 + x2 = 0 + 1.93877551 Reorder the terms: -1.93877551 + 1.93877551 + -5x + x2 = 0 + 1.93877551 Combine like terms: -1.93877551 + 1.93877551 = 0.00000000 0.00000000 + -5x + x2 = 0 + 1.93877551 -5x + x2 = 0 + 1.93877551 Combine like terms: 0 + 1.93877551 = 1.93877551 -5x + x2 = 1.93877551 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 = 1.93877551 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 1.93877551 + 6.25 Combine like terms: 1.93877551 + 6.25 = 8.18877551 6.25 + -5x + x2 = 8.18877551 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 8.18877551 Calculate the square root of the right side: 2.861603661 Break this problem into two subproblems by setting (x + -2.5) equal to 2.861603661 and -2.861603661.Subproblem 1
x + -2.5 = 2.861603661 Simplifying x + -2.5 = 2.861603661 Reorder the terms: -2.5 + x = 2.861603661 Solving -2.5 + x = 2.861603661 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 = 2.861603661 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.861603661 + 2.5 x = 2.861603661 + 2.5 Combine like terms: 2.861603661 + 2.5 = 5.361603661 x = 5.361603661 Simplifying x = 5.361603661Subproblem 2
x + -2.5 = -2.861603661 Simplifying x + -2.5 = -2.861603661 Reorder the terms: -2.5 + x = -2.861603661 Solving -2.5 + x = -2.861603661 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 = -2.861603661 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.861603661 + 2.5 x = -2.861603661 + 2.5 Combine like terms: -2.861603661 + 2.5 = -0.361603661 x = -0.361603661 Simplifying x = -0.361603661Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.361603661, -0.361603661}
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