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Simplifying 4.9x2 + 6x + -1.25 = 0 Reorder the terms: -1.25 + 6x + 4.9x2 = 0 Solving -1.25 + 6x + 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'. -0.2551020408 + 1.224489796x + x2 = 0 Move the constant term to the right: Add '0.2551020408' to each side of the equation. -0.2551020408 + 1.224489796x + 0.2551020408 + x2 = 0 + 0.2551020408 Reorder the terms: -0.2551020408 + 0.2551020408 + 1.224489796x + x2 = 0 + 0.2551020408 Combine like terms: -0.2551020408 + 0.2551020408 = 0.0000000000 0.0000000000 + 1.224489796x + x2 = 0 + 0.2551020408 1.224489796x + x2 = 0 + 0.2551020408 Combine like terms: 0 + 0.2551020408 = 0.2551020408 1.224489796x + x2 = 0.2551020408 The x term is 1.224489796x. Take half its coefficient (0.612244898). Square it (0.3748438151) and add it to both sides. Add '0.3748438151' to each side of the equation. 1.224489796x + 0.3748438151 + x2 = 0.2551020408 + 0.3748438151 Reorder the terms: 0.3748438151 + 1.224489796x + x2 = 0.2551020408 + 0.3748438151 Combine like terms: 0.2551020408 + 0.3748438151 = 0.6299458559 0.3748438151 + 1.224489796x + x2 = 0.6299458559 Factor a perfect square on the left side: (x + 0.612244898)(x + 0.612244898) = 0.6299458559 Calculate the square root of the right side: 0.793691285 Break this problem into two subproblems by setting (x + 0.612244898) equal to 0.793691285 and -0.793691285.Subproblem 1
x + 0.612244898 = 0.793691285 Simplifying x + 0.612244898 = 0.793691285 Reorder the terms: 0.612244898 + x = 0.793691285 Solving 0.612244898 + x = 0.793691285 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.612244898' to each side of the equation. 0.612244898 + -0.612244898 + x = 0.793691285 + -0.612244898 Combine like terms: 0.612244898 + -0.612244898 = 0.000000000 0.000000000 + x = 0.793691285 + -0.612244898 x = 0.793691285 + -0.612244898 Combine like terms: 0.793691285 + -0.612244898 = 0.181446387 x = 0.181446387 Simplifying x = 0.181446387Subproblem 2
x + 0.612244898 = -0.793691285 Simplifying x + 0.612244898 = -0.793691285 Reorder the terms: 0.612244898 + x = -0.793691285 Solving 0.612244898 + x = -0.793691285 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.612244898' to each side of the equation. 0.612244898 + -0.612244898 + x = -0.793691285 + -0.612244898 Combine like terms: 0.612244898 + -0.612244898 = 0.000000000 0.000000000 + x = -0.793691285 + -0.612244898 x = -0.793691285 + -0.612244898 Combine like terms: -0.793691285 + -0.612244898 = -1.405936183 x = -1.405936183 Simplifying x = -1.405936183Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.181446387, -1.405936183}
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