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Simplifying 2x2 + -35x + 54 = 0 Reorder the terms: 54 + -35x + 2x2 = 0 Solving 54 + -35x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 27 + -17.5x + x2 = 0 Move the constant term to the right: Add '-27' to each side of the equation. 27 + -17.5x + -27 + x2 = 0 + -27 Reorder the terms: 27 + -27 + -17.5x + x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -17.5x + x2 = 0 + -27 -17.5x + x2 = 0 + -27 Combine like terms: 0 + -27 = -27 -17.5x + x2 = -27 The x term is -17.5x. Take half its coefficient (-8.75). Square it (76.5625) and add it to both sides. Add '76.5625' to each side of the equation. -17.5x + 76.5625 + x2 = -27 + 76.5625 Reorder the terms: 76.5625 + -17.5x + x2 = -27 + 76.5625 Combine like terms: -27 + 76.5625 = 49.5625 76.5625 + -17.5x + x2 = 49.5625 Factor a perfect square on the left side: (x + -8.75)(x + -8.75) = 49.5625 Calculate the square root of the right side: 7.04006392 Break this problem into two subproblems by setting (x + -8.75) equal to 7.04006392 and -7.04006392.Subproblem 1
x + -8.75 = 7.04006392 Simplifying x + -8.75 = 7.04006392 Reorder the terms: -8.75 + x = 7.04006392 Solving -8.75 + x = 7.04006392 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.75' to each side of the equation. -8.75 + 8.75 + x = 7.04006392 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + x = 7.04006392 + 8.75 x = 7.04006392 + 8.75 Combine like terms: 7.04006392 + 8.75 = 15.79006392 x = 15.79006392 Simplifying x = 15.79006392Subproblem 2
x + -8.75 = -7.04006392 Simplifying x + -8.75 = -7.04006392 Reorder the terms: -8.75 + x = -7.04006392 Solving -8.75 + x = -7.04006392 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.75' to each side of the equation. -8.75 + 8.75 + x = -7.04006392 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + x = -7.04006392 + 8.75 x = -7.04006392 + 8.75 Combine like terms: -7.04006392 + 8.75 = 1.70993608 x = 1.70993608 Simplifying x = 1.70993608Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.79006392, 1.70993608}
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