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Simplifying 0 = 4.9x2 + 10.883x + -4.953 Reorder the terms: 0 = -4.953 + 10.883x + 4.9x2 Solving 0 = -4.953 + 10.883x + 4.9x2 Solving for variable 'x'. Combine like terms: 0 + 4.953 = 4.953 4.953 + -10.883x + -4.9x2 = -4.953 + 10.883x + 4.9x2 + 4.953 + -10.883x + -4.9x2 Reorder the terms: 4.953 + -10.883x + -4.9x2 = -4.953 + 4.953 + 10.883x + -10.883x + 4.9x2 + -4.9x2 Combine like terms: -4.953 + 4.953 = 0.000 4.953 + -10.883x + -4.9x2 = 0.000 + 10.883x + -10.883x + 4.9x2 + -4.9x2 4.953 + -10.883x + -4.9x2 = 10.883x + -10.883x + 4.9x2 + -4.9x2 Combine like terms: 10.883x + -10.883x = 0.000 4.953 + -10.883x + -4.9x2 = 0.000 + 4.9x2 + -4.9x2 4.953 + -10.883x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 4.953 + -10.883x + -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'. -1.010816327 + 2.221020408x + x2 = 0 Move the constant term to the right: Add '1.010816327' to each side of the equation. -1.010816327 + 2.221020408x + 1.010816327 + x2 = 0 + 1.010816327 Reorder the terms: -1.010816327 + 1.010816327 + 2.221020408x + x2 = 0 + 1.010816327 Combine like terms: -1.010816327 + 1.010816327 = 0.000000000 0.000000000 + 2.221020408x + x2 = 0 + 1.010816327 2.221020408x + x2 = 0 + 1.010816327 Combine like terms: 0 + 1.010816327 = 1.010816327 2.221020408x + x2 = 1.010816327 The x term is 2.221020408x. Take half its coefficient (1.110510204). Square it (1.233232913) and add it to both sides. Add '1.233232913' to each side of the equation. 2.221020408x + 1.233232913 + x2 = 1.010816327 + 1.233232913 Reorder the terms: 1.233232913 + 2.221020408x + x2 = 1.010816327 + 1.233232913 Combine like terms: 1.010816327 + 1.233232913 = 2.24404924 1.233232913 + 2.221020408x + x2 = 2.24404924 Factor a perfect square on the left side: (x + 1.110510204)(x + 1.110510204) = 2.24404924 Calculate the square root of the right side: 1.4980151 Break this problem into two subproblems by setting (x + 1.110510204) equal to 1.4980151 and -1.4980151.Subproblem 1
x + 1.110510204 = 1.4980151 Simplifying x + 1.110510204 = 1.4980151 Reorder the terms: 1.110510204 + x = 1.4980151 Solving 1.110510204 + x = 1.4980151 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.110510204' to each side of the equation. 1.110510204 + -1.110510204 + x = 1.4980151 + -1.110510204 Combine like terms: 1.110510204 + -1.110510204 = 0.000000000 0.000000000 + x = 1.4980151 + -1.110510204 x = 1.4980151 + -1.110510204 Combine like terms: 1.4980151 + -1.110510204 = 0.387504896 x = 0.387504896 Simplifying x = 0.387504896Subproblem 2
x + 1.110510204 = -1.4980151 Simplifying x + 1.110510204 = -1.4980151 Reorder the terms: 1.110510204 + x = -1.4980151 Solving 1.110510204 + x = -1.4980151 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.110510204' to each side of the equation. 1.110510204 + -1.110510204 + x = -1.4980151 + -1.110510204 Combine like terms: 1.110510204 + -1.110510204 = 0.000000000 0.000000000 + x = -1.4980151 + -1.110510204 x = -1.4980151 + -1.110510204 Combine like terms: -1.4980151 + -1.110510204 = -2.608525304 x = -2.608525304 Simplifying x = -2.608525304Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.387504896, -2.608525304}
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