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Simplifying -4.9x2 + 11x + 2 = 7.81 Reorder the terms: 2 + 11x + -4.9x2 = 7.81 Solving 2 + 11x + -4.9x2 = 7.81 Solving for variable 'x'. Reorder the terms: 2 + -7.81 + 11x + -4.9x2 = 7.81 + -7.81 Combine like terms: 2 + -7.81 = -5.81 -5.81 + 11x + -4.9x2 = 7.81 + -7.81 Combine like terms: 7.81 + -7.81 = 0.00 -5.81 + 11x + -4.9x2 = 0.00 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 1.185714286 + -2.244897959x + x2 = 0.0 Move the constant term to the right: Add '-1.185714286' to each side of the equation. 1.185714286 + -2.244897959x + -1.185714286 + x2 = 0.0 + -1.185714286 Reorder the terms: 1.185714286 + -1.185714286 + -2.244897959x + x2 = 0.0 + -1.185714286 Combine like terms: 1.185714286 + -1.185714286 = 0.000000000 0.000000000 + -2.244897959x + x2 = 0.0 + -1.185714286 -2.244897959x + x2 = 0.0 + -1.185714286 Combine like terms: 0.0 + -1.185714286 = -1.185714286 -2.244897959x + x2 = -1.185714286 The x term is -2.244897959x. Take half its coefficient (-1.12244898). Square it (1.259891713) and add it to both sides. Add '1.259891713' to each side of the equation. -2.244897959x + 1.259891713 + x2 = -1.185714286 + 1.259891713 Reorder the terms: 1.259891713 + -2.244897959x + x2 = -1.185714286 + 1.259891713 Combine like terms: -1.185714286 + 1.259891713 = 0.074177427 1.259891713 + -2.244897959x + x2 = 0.074177427 Factor a perfect square on the left side: (x + -1.12244898)(x + -1.12244898) = 0.074177427 Calculate the square root of the right side: 0.272355332 Break this problem into two subproblems by setting (x + -1.12244898) equal to 0.272355332 and -0.272355332.Subproblem 1
x + -1.12244898 = 0.272355332 Simplifying x + -1.12244898 = 0.272355332 Reorder the terms: -1.12244898 + x = 0.272355332 Solving -1.12244898 + x = 0.272355332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.12244898' to each side of the equation. -1.12244898 + 1.12244898 + x = 0.272355332 + 1.12244898 Combine like terms: -1.12244898 + 1.12244898 = 0.00000000 0.00000000 + x = 0.272355332 + 1.12244898 x = 0.272355332 + 1.12244898 Combine like terms: 0.272355332 + 1.12244898 = 1.394804312 x = 1.394804312 Simplifying x = 1.394804312Subproblem 2
x + -1.12244898 = -0.272355332 Simplifying x + -1.12244898 = -0.272355332 Reorder the terms: -1.12244898 + x = -0.272355332 Solving -1.12244898 + x = -0.272355332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.12244898' to each side of the equation. -1.12244898 + 1.12244898 + x = -0.272355332 + 1.12244898 Combine like terms: -1.12244898 + 1.12244898 = 0.00000000 0.00000000 + x = -0.272355332 + 1.12244898 x = -0.272355332 + 1.12244898 Combine like terms: -0.272355332 + 1.12244898 = 0.850093648 x = 0.850093648 Simplifying x = 0.850093648Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.394804312, 0.850093648}
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