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Simplifying 4.9x2 + 5x + -5 = 0 Reorder the terms: -5 + 5x + 4.9x2 = 0 Solving -5 + 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'. -1.020408163 + 1.020408163x + x2 = 0 Move the constant term to the right: Add '1.020408163' to each side of the equation. -1.020408163 + 1.020408163x + 1.020408163 + x2 = 0 + 1.020408163 Reorder the terms: -1.020408163 + 1.020408163 + 1.020408163x + x2 = 0 + 1.020408163 Combine like terms: -1.020408163 + 1.020408163 = 0.000000000 0.000000000 + 1.020408163x + x2 = 0 + 1.020408163 1.020408163x + x2 = 0 + 1.020408163 Combine like terms: 0 + 1.020408163 = 1.020408163 1.020408163x + x2 = 1.020408163 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 = 1.020408163 + 0.2603082048 Reorder the terms: 0.2603082048 + 1.020408163x + x2 = 1.020408163 + 0.2603082048 Combine like terms: 1.020408163 + 0.2603082048 = 1.2807163678 0.2603082048 + 1.020408163x + x2 = 1.2807163678 Factor a perfect square on the left side: (x + 0.5102040815)(x + 0.5102040815) = 1.2807163678 Calculate the square root of the right side: 1.131687398 Break this problem into two subproblems by setting (x + 0.5102040815) equal to 1.131687398 and -1.131687398.Subproblem 1
x + 0.5102040815 = 1.131687398 Simplifying x + 0.5102040815 = 1.131687398 Reorder the terms: 0.5102040815 + x = 1.131687398 Solving 0.5102040815 + x = 1.131687398 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 = 1.131687398 + -0.5102040815 Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000 0.0000000000 + x = 1.131687398 + -0.5102040815 x = 1.131687398 + -0.5102040815 Combine like terms: 1.131687398 + -0.5102040815 = 0.6214833165 x = 0.6214833165 Simplifying x = 0.6214833165Subproblem 2
x + 0.5102040815 = -1.131687398 Simplifying x + 0.5102040815 = -1.131687398 Reorder the terms: 0.5102040815 + x = -1.131687398 Solving 0.5102040815 + x = -1.131687398 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 = -1.131687398 + -0.5102040815 Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000 0.0000000000 + x = -1.131687398 + -0.5102040815 x = -1.131687398 + -0.5102040815 Combine like terms: -1.131687398 + -0.5102040815 = -1.6418914795 x = -1.6418914795 Simplifying x = -1.6418914795Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6214833165, -1.6418914795}
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