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Simplifying 4.9x2 + -5x + -80 = 0 Reorder the terms: -80 + -5x + 4.9x2 = 0 Solving -80 + -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'. -16.32653061 + -1.020408163x + x2 = 0 Move the constant term to the right: Add '16.32653061' to each side of the equation. -16.32653061 + -1.020408163x + 16.32653061 + x2 = 0 + 16.32653061 Reorder the terms: -16.32653061 + 16.32653061 + -1.020408163x + x2 = 0 + 16.32653061 Combine like terms: -16.32653061 + 16.32653061 = 0.00000000 0.00000000 + -1.020408163x + x2 = 0 + 16.32653061 -1.020408163x + x2 = 0 + 16.32653061 Combine like terms: 0 + 16.32653061 = 16.32653061 -1.020408163x + x2 = 16.32653061 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 = 16.32653061 + 0.2603082048 Reorder the terms: 0.2603082048 + -1.020408163x + x2 = 16.32653061 + 0.2603082048 Combine like terms: 16.32653061 + 0.2603082048 = 16.5868388148 0.2603082048 + -1.020408163x + x2 = 16.5868388148 Factor a perfect square on the left side: (x + -0.5102040815)(x + -0.5102040815) = 16.5868388148 Calculate the square root of the right side: 4.072694294 Break this problem into two subproblems by setting (x + -0.5102040815) equal to 4.072694294 and -4.072694294.Subproblem 1
x + -0.5102040815 = 4.072694294 Simplifying x + -0.5102040815 = 4.072694294 Reorder the terms: -0.5102040815 + x = 4.072694294 Solving -0.5102040815 + x = 4.072694294 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 = 4.072694294 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + x = 4.072694294 + 0.5102040815 x = 4.072694294 + 0.5102040815 Combine like terms: 4.072694294 + 0.5102040815 = 4.5828983755 x = 4.5828983755 Simplifying x = 4.5828983755Subproblem 2
x + -0.5102040815 = -4.072694294 Simplifying x + -0.5102040815 = -4.072694294 Reorder the terms: -0.5102040815 + x = -4.072694294 Solving -0.5102040815 + x = -4.072694294 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 = -4.072694294 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + x = -4.072694294 + 0.5102040815 x = -4.072694294 + 0.5102040815 Combine like terms: -4.072694294 + 0.5102040815 = -3.5624902125 x = -3.5624902125 Simplifying x = -3.5624902125Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.5828983755, -3.5624902125}
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