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Simplifying 0 = 30 + -56x + 3.5x2 Solving 0 = 30 + -56x + 3.5x2 Solving for variable 'x'. Combine like terms: 0 + -30 = -30 -30 + 56x + -3.5x2 = 30 + -56x + 3.5x2 + -30 + 56x + -3.5x2 Reorder the terms: -30 + 56x + -3.5x2 = 30 + -30 + -56x + 56x + 3.5x2 + -3.5x2 Combine like terms: 30 + -30 = 0 -30 + 56x + -3.5x2 = 0 + -56x + 56x + 3.5x2 + -3.5x2 -30 + 56x + -3.5x2 = -56x + 56x + 3.5x2 + -3.5x2 Combine like terms: -56x + 56x = 0 -30 + 56x + -3.5x2 = 0 + 3.5x2 + -3.5x2 -30 + 56x + -3.5x2 = 3.5x2 + -3.5x2 Combine like terms: 3.5x2 + -3.5x2 = 0.0 -30 + 56x + -3.5x2 = 0.0 Begin completing the square. Divide all terms by -3.5 the coefficient of the squared term: Divide each side by '-3.5'. 8.571428571 + -16x + x2 = 0 Move the constant term to the right: Add '-8.571428571' to each side of the equation. 8.571428571 + -16x + -8.571428571 + x2 = 0 + -8.571428571 Reorder the terms: 8.571428571 + -8.571428571 + -16x + x2 = 0 + -8.571428571 Combine like terms: 8.571428571 + -8.571428571 = 0.000000000 0.000000000 + -16x + x2 = 0 + -8.571428571 -16x + x2 = 0 + -8.571428571 Combine like terms: 0 + -8.571428571 = -8.571428571 -16x + x2 = -8.571428571 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = -8.571428571 + 64 Reorder the terms: 64 + -16x + x2 = -8.571428571 + 64 Combine like terms: -8.571428571 + 64 = 55.428571429 64 + -16x + x2 = 55.428571429 Factor a perfect square on the left side: (x + -8)(x + -8) = 55.428571429 Calculate the square root of the right side: 7.445036698 Break this problem into two subproblems by setting (x + -8) equal to 7.445036698 and -7.445036698.Subproblem 1
x + -8 = 7.445036698 Simplifying x + -8 = 7.445036698 Reorder the terms: -8 + x = 7.445036698 Solving -8 + x = 7.445036698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 7.445036698 + 8 Combine like terms: -8 + 8 = 0 0 + x = 7.445036698 + 8 x = 7.445036698 + 8 Combine like terms: 7.445036698 + 8 = 15.445036698 x = 15.445036698 Simplifying x = 15.445036698Subproblem 2
x + -8 = -7.445036698 Simplifying x + -8 = -7.445036698 Reorder the terms: -8 + x = -7.445036698 Solving -8 + x = -7.445036698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -7.445036698 + 8 Combine like terms: -8 + 8 = 0 0 + x = -7.445036698 + 8 x = -7.445036698 + 8 Combine like terms: -7.445036698 + 8 = 0.554963302 x = 0.554963302 Simplifying x = 0.554963302Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.445036698, 0.554963302}
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