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Simplifying 0 = -4.9x2 + 7x + 140 Reorder the terms: 0 = 140 + 7x + -4.9x2 Solving 0 = 140 + 7x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -140 = -140 -140 + -7x + 4.9x2 = 140 + 7x + -4.9x2 + -140 + -7x + 4.9x2 Reorder the terms: -140 + -7x + 4.9x2 = 140 + -140 + 7x + -7x + -4.9x2 + 4.9x2 Combine like terms: 140 + -140 = 0 -140 + -7x + 4.9x2 = 0 + 7x + -7x + -4.9x2 + 4.9x2 -140 + -7x + 4.9x2 = 7x + -7x + -4.9x2 + 4.9x2 Combine like terms: 7x + -7x = 0 -140 + -7x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -140 + -7x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -140 + -7x + 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'. -28.57142857 + -1.428571429x + x2 = 0 Move the constant term to the right: Add '28.57142857' to each side of the equation. -28.57142857 + -1.428571429x + 28.57142857 + x2 = 0 + 28.57142857 Reorder the terms: -28.57142857 + 28.57142857 + -1.428571429x + x2 = 0 + 28.57142857 Combine like terms: -28.57142857 + 28.57142857 = 0.00000000 0.00000000 + -1.428571429x + x2 = 0 + 28.57142857 -1.428571429x + x2 = 0 + 28.57142857 Combine like terms: 0 + 28.57142857 = 28.57142857 -1.428571429x + x2 = 28.57142857 The x term is -1.428571429x. Take half its coefficient (-0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. -1.428571429x + 0.5102040819 + x2 = 28.57142857 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429x + x2 = 28.57142857 + 0.5102040819 Combine like terms: 28.57142857 + 0.5102040819 = 29.0816326519 0.5102040819 + -1.428571429x + x2 = 29.0816326519 Factor a perfect square on the left side: (x + -0.7142857145)(x + -0.7142857145) = 29.0816326519 Calculate the square root of the right side: 5.392738882 Break this problem into two subproblems by setting (x + -0.7142857145) equal to 5.392738882 and -5.392738882.Subproblem 1
x + -0.7142857145 = 5.392738882 Simplifying x + -0.7142857145 = 5.392738882 Reorder the terms: -0.7142857145 + x = 5.392738882 Solving -0.7142857145 + x = 5.392738882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = 5.392738882 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = 5.392738882 + 0.7142857145 x = 5.392738882 + 0.7142857145 Combine like terms: 5.392738882 + 0.7142857145 = 6.1070245965 x = 6.1070245965 Simplifying x = 6.1070245965Subproblem 2
x + -0.7142857145 = -5.392738882 Simplifying x + -0.7142857145 = -5.392738882 Reorder the terms: -0.7142857145 + x = -5.392738882 Solving -0.7142857145 + x = -5.392738882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = -5.392738882 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = -5.392738882 + 0.7142857145 x = -5.392738882 + 0.7142857145 Combine like terms: -5.392738882 + 0.7142857145 = -4.6784531675 x = -4.6784531675 Simplifying x = -4.6784531675Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.1070245965, -4.6784531675}
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