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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 = 0.1197417743 0.3748438151 + -1.224489796x + x2 = 0.1197417743 Factor a perfect square on the left side: (x + -0.612244898)(x + -0.612244898) = 0.1197417743 Calculate the square root of the right side: 0.346037244 Break this problem into two subproblems by setting (x + -0.612244898) equal to 0.346037244 and -0.346037244.Subproblem 1
x + -0.612244898 = 0.346037244 Simplifying x + -0.612244898 = 0.346037244 Reorder the terms: -0.612244898 + x = 0.346037244 Solving -0.612244898 + x = 0.346037244 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 = 0.346037244 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + x = 0.346037244 + 0.612244898 x = 0.346037244 + 0.612244898 Combine like terms: 0.346037244 + 0.612244898 = 0.958282142 x = 0.958282142 Simplifying x = 0.958282142Subproblem 2
x + -0.612244898 = -0.346037244 Simplifying x + -0.612244898 = -0.346037244 Reorder the terms: -0.612244898 + x = -0.346037244 Solving -0.612244898 + x = -0.346037244 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 = -0.346037244 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + x = -0.346037244 + 0.612244898 x = -0.346037244 + 0.612244898 Combine like terms: -0.346037244 + 0.612244898 = 0.266207654 x = 0.266207654 Simplifying x = 0.266207654Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.958282142, 0.266207654}
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