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Simplifying 4.9x2 + 5x + -300 = 0 Reorder the terms: -300 + 5x + 4.9x2 = 0 Solving -300 + 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'. -61.2244898 + 1.020408163x + x2 = 0 Move the constant term to the right: Add '61.2244898' to each side of the equation. -61.2244898 + 1.020408163x + 61.2244898 + x2 = 0 + 61.2244898 Reorder the terms: -61.2244898 + 61.2244898 + 1.020408163x + x2 = 0 + 61.2244898 Combine like terms: -61.2244898 + 61.2244898 = 0.0000000 0.0000000 + 1.020408163x + x2 = 0 + 61.2244898 1.020408163x + x2 = 0 + 61.2244898 Combine like terms: 0 + 61.2244898 = 61.2244898 1.020408163x + x2 = 61.2244898 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 = 61.2244898 + 0.2603082048 Reorder the terms: 0.2603082048 + 1.020408163x + x2 = 61.2244898 + 0.2603082048 Combine like terms: 61.2244898 + 0.2603082048 = 61.4847980048 0.2603082048 + 1.020408163x + x2 = 61.4847980048 Factor a perfect square on the left side: (x + 0.5102040815)(x + 0.5102040815) = 61.4847980048 Calculate the square root of the right side: 7.841224267 Break this problem into two subproblems by setting (x + 0.5102040815) equal to 7.841224267 and -7.841224267.Subproblem 1
x + 0.5102040815 = 7.841224267 Simplifying x + 0.5102040815 = 7.841224267 Reorder the terms: 0.5102040815 + x = 7.841224267 Solving 0.5102040815 + x = 7.841224267 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 = 7.841224267 + -0.5102040815 Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000 0.0000000000 + x = 7.841224267 + -0.5102040815 x = 7.841224267 + -0.5102040815 Combine like terms: 7.841224267 + -0.5102040815 = 7.3310201855 x = 7.3310201855 Simplifying x = 7.3310201855Subproblem 2
x + 0.5102040815 = -7.841224267 Simplifying x + 0.5102040815 = -7.841224267 Reorder the terms: 0.5102040815 + x = -7.841224267 Solving 0.5102040815 + x = -7.841224267 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 = -7.841224267 + -0.5102040815 Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000 0.0000000000 + x = -7.841224267 + -0.5102040815 x = -7.841224267 + -0.5102040815 Combine like terms: -7.841224267 + -0.5102040815 = -8.3514283485 x = -8.3514283485 Simplifying x = -8.3514283485Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.3310201855, -8.3514283485}
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