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Simplifying -4.9x2 + 5x + 218 = 0 Reorder the terms: 218 + 5x + -4.9x2 = 0 Solving 218 + 5x + -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'. -44.48979592 + -1.020408163x + x2 = 0 Move the constant term to the right: Add '44.48979592' to each side of the equation. -44.48979592 + -1.020408163x + 44.48979592 + x2 = 0 + 44.48979592 Reorder the terms: -44.48979592 + 44.48979592 + -1.020408163x + x2 = 0 + 44.48979592 Combine like terms: -44.48979592 + 44.48979592 = 0.00000000 0.00000000 + -1.020408163x + x2 = 0 + 44.48979592 -1.020408163x + x2 = 0 + 44.48979592 Combine like terms: 0 + 44.48979592 = 44.48979592 -1.020408163x + x2 = 44.48979592 The x term is -1.020408163x. Take half its coefficient (-0.5102040815). Square it (0.2603082048) and add it to both sides. Add '0.2603082048' to each side of the equation. -1.020408163x + 0.2603082048 + x2 = 44.48979592 + 0.2603082048 Reorder the terms: 0.2603082048 + -1.020408163x + x2 = 44.48979592 + 0.2603082048 Combine like terms: 44.48979592 + 0.2603082048 = 44.7501041248 0.2603082048 + -1.020408163x + x2 = 44.7501041248 Factor a perfect square on the left side: (x + -0.5102040815)(x + -0.5102040815) = 44.7501041248 Calculate the square root of the right side: 6.689551863 Break this problem into two subproblems by setting (x + -0.5102040815) equal to 6.689551863 and -6.689551863.Subproblem 1
x + -0.5102040815 = 6.689551863 Simplifying x + -0.5102040815 = 6.689551863 Reorder the terms: -0.5102040815 + x = 6.689551863 Solving -0.5102040815 + x = 6.689551863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5102040815' to each side of the equation. -0.5102040815 + 0.5102040815 + x = 6.689551863 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + x = 6.689551863 + 0.5102040815 x = 6.689551863 + 0.5102040815 Combine like terms: 6.689551863 + 0.5102040815 = 7.1997559445 x = 7.1997559445 Simplifying x = 7.1997559445Subproblem 2
x + -0.5102040815 = -6.689551863 Simplifying x + -0.5102040815 = -6.689551863 Reorder the terms: -0.5102040815 + x = -6.689551863 Solving -0.5102040815 + x = -6.689551863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5102040815' to each side of the equation. -0.5102040815 + 0.5102040815 + x = -6.689551863 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + x = -6.689551863 + 0.5102040815 x = -6.689551863 + 0.5102040815 Combine like terms: -6.689551863 + 0.5102040815 = -6.1793477815 x = -6.1793477815 Simplifying x = -6.1793477815Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.1997559445, -6.1793477815}
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