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Simplifying 0 = 12 + 6x + -4.9x2 Solving 0 = 12 + 6x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -12 = -12 -12 + -6x + 4.9x2 = 12 + 6x + -4.9x2 + -12 + -6x + 4.9x2 Reorder the terms: -12 + -6x + 4.9x2 = 12 + -12 + 6x + -6x + -4.9x2 + 4.9x2 Combine like terms: 12 + -12 = 0 -12 + -6x + 4.9x2 = 0 + 6x + -6x + -4.9x2 + 4.9x2 -12 + -6x + 4.9x2 = 6x + -6x + -4.9x2 + 4.9x2 Combine like terms: 6x + -6x = 0 -12 + -6x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -12 + -6x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -12 + -6x + 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'. -2.448979592 + -1.224489796x + x2 = 0 Move the constant term to the right: Add '2.448979592' to each side of the equation. -2.448979592 + -1.224489796x + 2.448979592 + x2 = 0 + 2.448979592 Reorder the terms: -2.448979592 + 2.448979592 + -1.224489796x + x2 = 0 + 2.448979592 Combine like terms: -2.448979592 + 2.448979592 = 0.000000000 0.000000000 + -1.224489796x + x2 = 0 + 2.448979592 -1.224489796x + x2 = 0 + 2.448979592 Combine like terms: 0 + 2.448979592 = 2.448979592 -1.224489796x + x2 = 2.448979592 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 = 2.448979592 + 0.3748438151 Reorder the terms: 0.3748438151 + -1.224489796x + x2 = 2.448979592 + 0.3748438151 Combine like terms: 2.448979592 + 0.3748438151 = 2.8238234071 0.3748438151 + -1.224489796x + x2 = 2.8238234071 Factor a perfect square on the left side: (x + -0.612244898)(x + -0.612244898) = 2.8238234071 Calculate the square root of the right side: 1.68042358 Break this problem into two subproblems by setting (x + -0.612244898) equal to 1.68042358 and -1.68042358.Subproblem 1
x + -0.612244898 = 1.68042358 Simplifying x + -0.612244898 = 1.68042358 Reorder the terms: -0.612244898 + x = 1.68042358 Solving -0.612244898 + x = 1.68042358 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 = 1.68042358 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + x = 1.68042358 + 0.612244898 x = 1.68042358 + 0.612244898 Combine like terms: 1.68042358 + 0.612244898 = 2.292668478 x = 2.292668478 Simplifying x = 2.292668478Subproblem 2
x + -0.612244898 = -1.68042358 Simplifying x + -0.612244898 = -1.68042358 Reorder the terms: -0.612244898 + x = -1.68042358 Solving -0.612244898 + x = -1.68042358 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 = -1.68042358 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + x = -1.68042358 + 0.612244898 x = -1.68042358 + 0.612244898 Combine like terms: -1.68042358 + 0.612244898 = -1.068178682 x = -1.068178682 Simplifying x = -1.068178682Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.292668478, -1.068178682}
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