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Simplifying 49x2 + 6x + -4 = 0 Reorder the terms: -4 + 6x + 49x2 = 0 Solving -4 + 6x + 49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.08163265306 + 0.1224489796x + x2 = 0 Move the constant term to the right: Add '0.08163265306' to each side of the equation. -0.08163265306 + 0.1224489796x + 0.08163265306 + x2 = 0 + 0.08163265306 Reorder the terms: -0.08163265306 + 0.08163265306 + 0.1224489796x + x2 = 0 + 0.08163265306 Combine like terms: -0.08163265306 + 0.08163265306 = 0.00000000000 0.00000000000 + 0.1224489796x + x2 = 0 + 0.08163265306 0.1224489796x + x2 = 0 + 0.08163265306 Combine like terms: 0 + 0.08163265306 = 0.08163265306 0.1224489796x + x2 = 0.08163265306 The x term is 0.1224489796x. Take half its coefficient (0.0612244898). Square it (0.003748438151) and add it to both sides. Add '0.003748438151' to each side of the equation. 0.1224489796x + 0.003748438151 + x2 = 0.08163265306 + 0.003748438151 Reorder the terms: 0.003748438151 + 0.1224489796x + x2 = 0.08163265306 + 0.003748438151 Combine like terms: 0.08163265306 + 0.003748438151 = 0.085381091211 0.003748438151 + 0.1224489796x + x2 = 0.085381091211 Factor a perfect square on the left side: (x + 0.0612244898)(x + 0.0612244898) = 0.085381091211 Calculate the square root of the right side: 0.29220043 Break this problem into two subproblems by setting (x + 0.0612244898) equal to 0.29220043 and -0.29220043.Subproblem 1
x + 0.0612244898 = 0.29220043 Simplifying x + 0.0612244898 = 0.29220043 Reorder the terms: 0.0612244898 + x = 0.29220043 Solving 0.0612244898 + x = 0.29220043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0612244898' to each side of the equation. 0.0612244898 + -0.0612244898 + x = 0.29220043 + -0.0612244898 Combine like terms: 0.0612244898 + -0.0612244898 = 0.0000000000 0.0000000000 + x = 0.29220043 + -0.0612244898 x = 0.29220043 + -0.0612244898 Combine like terms: 0.29220043 + -0.0612244898 = 0.2309759402 x = 0.2309759402 Simplifying x = 0.2309759402Subproblem 2
x + 0.0612244898 = -0.29220043 Simplifying x + 0.0612244898 = -0.29220043 Reorder the terms: 0.0612244898 + x = -0.29220043 Solving 0.0612244898 + x = -0.29220043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0612244898' to each side of the equation. 0.0612244898 + -0.0612244898 + x = -0.29220043 + -0.0612244898 Combine like terms: 0.0612244898 + -0.0612244898 = 0.0000000000 0.0000000000 + x = -0.29220043 + -0.0612244898 x = -0.29220043 + -0.0612244898 Combine like terms: -0.29220043 + -0.0612244898 = -0.3534249198 x = -0.3534249198 Simplifying x = -0.3534249198Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2309759402, -0.3534249198}
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