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Simplifying 395x * 195x + 95x = 22 Reorder the terms for easier multiplication: 395 * 195x * x + 95x = 22 Multiply 395 * 195 77025x * x + 95x = 22 Multiply x * x 77025x2 + 95x = 22 Reorder the terms: 95x + 77025x2 = 22 Solving 95x + 77025x2 = 22 Solving for variable 'x'. Reorder the terms: -22 + 95x + 77025x2 = 22 + -22 Combine like terms: 22 + -22 = 0 -22 + 95x + 77025x2 = 0 Begin completing the square. Divide all terms by 77025 the coefficient of the squared term: Divide each side by '77025'. -0.0002856215514 + 0.00123336579x + x2 = 0 Move the constant term to the right: Add '0.0002856215514' to each side of the equation. -0.0002856215514 + 0.00123336579x + 0.0002856215514 + x2 = 0 + 0.0002856215514 Reorder the terms: -0.0002856215514 + 0.0002856215514 + 0.00123336579x + x2 = 0 + 0.0002856215514 Combine like terms: -0.0002856215514 + 0.0002856215514 = 0.0000000000000 0.0000000000000 + 0.00123336579x + x2 = 0 + 0.0002856215514 0.00123336579x + x2 = 0 + 0.0002856215514 Combine like terms: 0 + 0.0002856215514 = 0.0002856215514 0.00123336579x + x2 = 0.0002856215514 The x term is 0.00123336579x. Take half its coefficient (0.000616682895). Square it (0.0000003802977930) and add it to both sides. Add '0.0000003802977930' to each side of the equation. 0.00123336579x + 0.0000003802977930 + x2 = 0.0002856215514 + 0.0000003802977930 Reorder the terms: 0.0000003802977930 + 0.00123336579x + x2 = 0.0002856215514 + 0.0000003802977930 Combine like terms: 0.0002856215514 + 0.0000003802977930 = 0.000286001849193 0.0000003802977930 + 0.00123336579x + x2 = 0.000286001849193 Factor a perfect square on the left side: (x + 0.000616682895)(x + 0.000616682895) = 0.000286001849193 Calculate the square root of the right side: 0.016911589 Break this problem into two subproblems by setting (x + 0.000616682895) equal to 0.016911589 and -0.016911589.Subproblem 1
x + 0.000616682895 = 0.016911589 Simplifying x + 0.000616682895 = 0.016911589 Reorder the terms: 0.000616682895 + x = 0.016911589 Solving 0.000616682895 + x = 0.016911589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000616682895' to each side of the equation. 0.000616682895 + -0.000616682895 + x = 0.016911589 + -0.000616682895 Combine like terms: 0.000616682895 + -0.000616682895 = 0.000000000000 0.000000000000 + x = 0.016911589 + -0.000616682895 x = 0.016911589 + -0.000616682895 Combine like terms: 0.016911589 + -0.000616682895 = 0.016294906105 x = 0.016294906105 Simplifying x = 0.016294906105Subproblem 2
x + 0.000616682895 = -0.016911589 Simplifying x + 0.000616682895 = -0.016911589 Reorder the terms: 0.000616682895 + x = -0.016911589 Solving 0.000616682895 + x = -0.016911589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000616682895' to each side of the equation. 0.000616682895 + -0.000616682895 + x = -0.016911589 + -0.000616682895 Combine like terms: 0.000616682895 + -0.000616682895 = 0.000000000000 0.000000000000 + x = -0.016911589 + -0.000616682895 x = -0.016911589 + -0.000616682895 Combine like terms: -0.016911589 + -0.000616682895 = -0.017528271895 x = -0.017528271895 Simplifying x = -0.017528271895Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.016294906105, -0.017528271895}
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