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Simplifying 4.9x2 + -68x = 4.1 Reorder the terms: -68x + 4.9x2 = 4.1 Solving -68x + 4.9x2 = 4.1 Solving for variable 'x'. Reorder the terms: -4.1 + -68x + 4.9x2 = 4.1 + -4.1 Combine like terms: 4.1 + -4.1 = 0.0 -4.1 + -68x + 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'. -0.8367346939 + -13.87755102x + x2 = 0 Move the constant term to the right: Add '0.8367346939' to each side of the equation. -0.8367346939 + -13.87755102x + 0.8367346939 + x2 = 0 + 0.8367346939 Reorder the terms: -0.8367346939 + 0.8367346939 + -13.87755102x + x2 = 0 + 0.8367346939 Combine like terms: -0.8367346939 + 0.8367346939 = 0.0000000000 0.0000000000 + -13.87755102x + x2 = 0 + 0.8367346939 -13.87755102x + x2 = 0 + 0.8367346939 Combine like terms: 0 + 0.8367346939 = 0.8367346939 -13.87755102x + x2 = 0.8367346939 The x term is -13.87755102x. Take half its coefficient (-6.93877551). Square it (48.14660558) and add it to both sides. Add '48.14660558' to each side of the equation. -13.87755102x + 48.14660558 + x2 = 0.8367346939 + 48.14660558 Reorder the terms: 48.14660558 + -13.87755102x + x2 = 0.8367346939 + 48.14660558 Combine like terms: 0.8367346939 + 48.14660558 = 48.9833402739 48.14660558 + -13.87755102x + x2 = 48.9833402739 Factor a perfect square on the left side: (x + -6.93877551)(x + -6.93877551) = 48.9833402739 Calculate the square root of the right side: 6.998809918 Break this problem into two subproblems by setting (x + -6.93877551) equal to 6.998809918 and -6.998809918.Subproblem 1
x + -6.93877551 = 6.998809918 Simplifying x + -6.93877551 = 6.998809918 Reorder the terms: -6.93877551 + x = 6.998809918 Solving -6.93877551 + x = 6.998809918 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.93877551' to each side of the equation. -6.93877551 + 6.93877551 + x = 6.998809918 + 6.93877551 Combine like terms: -6.93877551 + 6.93877551 = 0.00000000 0.00000000 + x = 6.998809918 + 6.93877551 x = 6.998809918 + 6.93877551 Combine like terms: 6.998809918 + 6.93877551 = 13.937585428 x = 13.937585428 Simplifying x = 13.937585428Subproblem 2
x + -6.93877551 = -6.998809918 Simplifying x + -6.93877551 = -6.998809918 Reorder the terms: -6.93877551 + x = -6.998809918 Solving -6.93877551 + x = -6.998809918 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.93877551' to each side of the equation. -6.93877551 + 6.93877551 + x = -6.998809918 + 6.93877551 Combine like terms: -6.93877551 + 6.93877551 = 0.00000000 0.00000000 + x = -6.998809918 + 6.93877551 x = -6.998809918 + 6.93877551 Combine like terms: -6.998809918 + 6.93877551 = -0.060034408 x = -0.060034408 Simplifying x = -0.060034408Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.937585428, -0.060034408}
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