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Simplifying 4x2 + -49x = 80 Reorder the terms: -49x + 4x2 = 80 Solving -49x + 4x2 = 80 Solving for variable 'x'. Reorder the terms: -80 + -49x + 4x2 = 80 + -80 Combine like terms: 80 + -80 = 0 -80 + -49x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -20 + -12.25x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -12.25x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -12.25x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -12.25x + x2 = 0 + 20 -12.25x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -12.25x + x2 = 20 The x term is -12.25x. Take half its coefficient (-6.125). Square it (37.515625) and add it to both sides. Add '37.515625' to each side of the equation. -12.25x + 37.515625 + x2 = 20 + 37.515625 Reorder the terms: 37.515625 + -12.25x + x2 = 20 + 37.515625 Combine like terms: 20 + 37.515625 = 57.515625 37.515625 + -12.25x + x2 = 57.515625 Factor a perfect square on the left side: (x + -6.125)(x + -6.125) = 57.515625 Calculate the square root of the right side: 7.583905656 Break this problem into two subproblems by setting (x + -6.125) equal to 7.583905656 and -7.583905656.Subproblem 1
x + -6.125 = 7.583905656 Simplifying x + -6.125 = 7.583905656 Reorder the terms: -6.125 + x = 7.583905656 Solving -6.125 + x = 7.583905656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.125' to each side of the equation. -6.125 + 6.125 + x = 7.583905656 + 6.125 Combine like terms: -6.125 + 6.125 = 0.000 0.000 + x = 7.583905656 + 6.125 x = 7.583905656 + 6.125 Combine like terms: 7.583905656 + 6.125 = 13.708905656 x = 13.708905656 Simplifying x = 13.708905656Subproblem 2
x + -6.125 = -7.583905656 Simplifying x + -6.125 = -7.583905656 Reorder the terms: -6.125 + x = -7.583905656 Solving -6.125 + x = -7.583905656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.125' to each side of the equation. -6.125 + 6.125 + x = -7.583905656 + 6.125 Combine like terms: -6.125 + 6.125 = 0.000 0.000 + x = -7.583905656 + 6.125 x = -7.583905656 + 6.125 Combine like terms: -7.583905656 + 6.125 = -1.458905656 x = -1.458905656 Simplifying x = -1.458905656Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.708905656, -1.458905656}
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