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Simplifying 0 = 4.9x2 + 5x + -1.6 Reorder the terms: 0 = -1.6 + 5x + 4.9x2 Solving 0 = -1.6 + 5x + 4.9x2 Solving for variable 'x'. Combine like terms: 0 + 1.6 = 1.6 1.6 + -5x + -4.9x2 = -1.6 + 5x + 4.9x2 + 1.6 + -5x + -4.9x2 Reorder the terms: 1.6 + -5x + -4.9x2 = -1.6 + 1.6 + 5x + -5x + 4.9x2 + -4.9x2 Combine like terms: -1.6 + 1.6 = 0.0 1.6 + -5x + -4.9x2 = 0.0 + 5x + -5x + 4.9x2 + -4.9x2 1.6 + -5x + -4.9x2 = 5x + -5x + 4.9x2 + -4.9x2 Combine like terms: 5x + -5x = 0 1.6 + -5x + -4.9x2 = 0 + 4.9x2 + -4.9x2 1.6 + -5x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 1.6 + -5x + -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'. -0.3265306122 + 1.020408163x + x2 = 0 Move the constant term to the right: Add '0.3265306122' to each side of the equation. -0.3265306122 + 1.020408163x + 0.3265306122 + x2 = 0 + 0.3265306122 Reorder the terms: -0.3265306122 + 0.3265306122 + 1.020408163x + x2 = 0 + 0.3265306122 Combine like terms: -0.3265306122 + 0.3265306122 = 0.0000000000 0.0000000000 + 1.020408163x + x2 = 0 + 0.3265306122 1.020408163x + x2 = 0 + 0.3265306122 Combine like terms: 0 + 0.3265306122 = 0.3265306122 1.020408163x + x2 = 0.3265306122 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 = 0.3265306122 + 0.2603082048 Reorder the terms: 0.2603082048 + 1.020408163x + x2 = 0.3265306122 + 0.2603082048 Combine like terms: 0.3265306122 + 0.2603082048 = 0.586838817 0.2603082048 + 1.020408163x + x2 = 0.586838817 Factor a perfect square on the left side: (x + 0.5102040815)(x + 0.5102040815) = 0.586838817 Calculate the square root of the right side: 0.766054056 Break this problem into two subproblems by setting (x + 0.5102040815) equal to 0.766054056 and -0.766054056.Subproblem 1
x + 0.5102040815 = 0.766054056 Simplifying x + 0.5102040815 = 0.766054056 Reorder the terms: 0.5102040815 + x = 0.766054056 Solving 0.5102040815 + x = 0.766054056 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 = 0.766054056 + -0.5102040815 Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000 0.0000000000 + x = 0.766054056 + -0.5102040815 x = 0.766054056 + -0.5102040815 Combine like terms: 0.766054056 + -0.5102040815 = 0.2558499745 x = 0.2558499745 Simplifying x = 0.2558499745Subproblem 2
x + 0.5102040815 = -0.766054056 Simplifying x + 0.5102040815 = -0.766054056 Reorder the terms: 0.5102040815 + x = -0.766054056 Solving 0.5102040815 + x = -0.766054056 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 = -0.766054056 + -0.5102040815 Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000 0.0000000000 + x = -0.766054056 + -0.5102040815 x = -0.766054056 + -0.5102040815 Combine like terms: -0.766054056 + -0.5102040815 = -1.2762581375 x = -1.2762581375 Simplifying x = -1.2762581375Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2558499745, -1.2762581375}
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