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Simplifying 50x2 + 19x + -4 = 0 Reorder the terms: -4 + 19x + 50x2 = 0 Solving -4 + 19x + 50x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. -0.08 + 0.38x + x2 = 0 Move the constant term to the right: Add '0.08' to each side of the equation. -0.08 + 0.38x + 0.08 + x2 = 0 + 0.08 Reorder the terms: -0.08 + 0.08 + 0.38x + x2 = 0 + 0.08 Combine like terms: -0.08 + 0.08 = 0.00 0.00 + 0.38x + x2 = 0 + 0.08 0.38x + x2 = 0 + 0.08 Combine like terms: 0 + 0.08 = 0.08 0.38x + x2 = 0.08 The x term is 0.38x. Take half its coefficient (0.19). Square it (0.0361) and add it to both sides. Add '0.0361' to each side of the equation. 0.38x + 0.0361 + x2 = 0.08 + 0.0361 Reorder the terms: 0.0361 + 0.38x + x2 = 0.08 + 0.0361 Combine like terms: 0.08 + 0.0361 = 0.1161 0.0361 + 0.38x + x2 = 0.1161 Factor a perfect square on the left side: (x + 0.19)(x + 0.19) = 0.1161 Calculate the square root of the right side: 0.340734501 Break this problem into two subproblems by setting (x + 0.19) equal to 0.340734501 and -0.340734501.Subproblem 1
x + 0.19 = 0.340734501 Simplifying x + 0.19 = 0.340734501 Reorder the terms: 0.19 + x = 0.340734501 Solving 0.19 + x = 0.340734501 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.19' to each side of the equation. 0.19 + -0.19 + x = 0.340734501 + -0.19 Combine like terms: 0.19 + -0.19 = 0.00 0.00 + x = 0.340734501 + -0.19 x = 0.340734501 + -0.19 Combine like terms: 0.340734501 + -0.19 = 0.150734501 x = 0.150734501 Simplifying x = 0.150734501Subproblem 2
x + 0.19 = -0.340734501 Simplifying x + 0.19 = -0.340734501 Reorder the terms: 0.19 + x = -0.340734501 Solving 0.19 + x = -0.340734501 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.19' to each side of the equation. 0.19 + -0.19 + x = -0.340734501 + -0.19 Combine like terms: 0.19 + -0.19 = 0.00 0.00 + x = -0.340734501 + -0.19 x = -0.340734501 + -0.19 Combine like terms: -0.340734501 + -0.19 = -0.530734501 x = -0.530734501 Simplifying x = -0.530734501Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.150734501, -0.530734501}
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