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Simplifying -4.9x2 + -7x + 250 = 0 Reorder the terms: 250 + -7x + -4.9x2 = 0 Solving 250 + -7x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -51.02040816 + 1.428571429x + x2 = 0 Move the constant term to the right: Add '51.02040816' to each side of the equation. -51.02040816 + 1.428571429x + 51.02040816 + x2 = 0 + 51.02040816 Reorder the terms: -51.02040816 + 51.02040816 + 1.428571429x + x2 = 0 + 51.02040816 Combine like terms: -51.02040816 + 51.02040816 = 0.00000000 0.00000000 + 1.428571429x + x2 = 0 + 51.02040816 1.428571429x + x2 = 0 + 51.02040816 Combine like terms: 0 + 51.02040816 = 51.02040816 1.428571429x + x2 = 51.02040816 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 = 51.02040816 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429x + x2 = 51.02040816 + 0.5102040819 Combine like terms: 51.02040816 + 0.5102040819 = 51.5306122419 0.5102040819 + 1.428571429x + x2 = 51.5306122419 Factor a perfect square on the left side: (x + 0.7142857145)(x + 0.7142857145) = 51.5306122419 Calculate the square root of the right side: 7.178482586 Break this problem into two subproblems by setting (x + 0.7142857145) equal to 7.178482586 and -7.178482586.Subproblem 1
x + 0.7142857145 = 7.178482586 Simplifying x + 0.7142857145 = 7.178482586 Reorder the terms: 0.7142857145 + x = 7.178482586 Solving 0.7142857145 + x = 7.178482586 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 = 7.178482586 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = 7.178482586 + -0.7142857145 x = 7.178482586 + -0.7142857145 Combine like terms: 7.178482586 + -0.7142857145 = 6.4641968715 x = 6.4641968715 Simplifying x = 6.4641968715Subproblem 2
x + 0.7142857145 = -7.178482586 Simplifying x + 0.7142857145 = -7.178482586 Reorder the terms: 0.7142857145 + x = -7.178482586 Solving 0.7142857145 + x = -7.178482586 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 = -7.178482586 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = -7.178482586 + -0.7142857145 x = -7.178482586 + -0.7142857145 Combine like terms: -7.178482586 + -0.7142857145 = -7.8927683005 x = -7.8927683005 Simplifying x = -7.8927683005Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.4641968715, -7.8927683005}
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