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Simplifying 4.9x2 + -5x + -115 = 0 Reorder the terms: -115 + -5x + 4.9x2 = 0 Solving -115 + -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'. -23.46938776 + -1.020408163x + x2 = 0 Move the constant term to the right: Add '23.46938776' to each side of the equation. -23.46938776 + -1.020408163x + 23.46938776 + x2 = 0 + 23.46938776 Reorder the terms: -23.46938776 + 23.46938776 + -1.020408163x + x2 = 0 + 23.46938776 Combine like terms: -23.46938776 + 23.46938776 = 0.00000000 0.00000000 + -1.020408163x + x2 = 0 + 23.46938776 -1.020408163x + x2 = 0 + 23.46938776 Combine like terms: 0 + 23.46938776 = 23.46938776 -1.020408163x + x2 = 23.46938776 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 = 23.46938776 + 0.2603082048 Reorder the terms: 0.2603082048 + -1.020408163x + x2 = 23.46938776 + 0.2603082048 Combine like terms: 23.46938776 + 0.2603082048 = 23.7296959648 0.2603082048 + -1.020408163x + x2 = 23.7296959648 Factor a perfect square on the left side: (x + -0.5102040815)(x + -0.5102040815) = 23.7296959648 Calculate the square root of the right side: 4.871313577 Break this problem into two subproblems by setting (x + -0.5102040815) equal to 4.871313577 and -4.871313577.Subproblem 1
x + -0.5102040815 = 4.871313577 Simplifying x + -0.5102040815 = 4.871313577 Reorder the terms: -0.5102040815 + x = 4.871313577 Solving -0.5102040815 + x = 4.871313577 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 = 4.871313577 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + x = 4.871313577 + 0.5102040815 x = 4.871313577 + 0.5102040815 Combine like terms: 4.871313577 + 0.5102040815 = 5.3815176585 x = 5.3815176585 Simplifying x = 5.3815176585Subproblem 2
x + -0.5102040815 = -4.871313577 Simplifying x + -0.5102040815 = -4.871313577 Reorder the terms: -0.5102040815 + x = -4.871313577 Solving -0.5102040815 + x = -4.871313577 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 = -4.871313577 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + x = -4.871313577 + 0.5102040815 x = -4.871313577 + 0.5102040815 Combine like terms: -4.871313577 + 0.5102040815 = -4.3611094955 x = -4.3611094955 Simplifying x = -4.3611094955Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.3815176585, -4.3611094955}
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