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Simplifying 19x2 + -18x + 1 = 0 Reorder the terms: 1 + -18x + 19x2 = 0 Solving 1 + -18x + 19x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. 0.05263157895 + -0.9473684211x + x2 = 0 Move the constant term to the right: Add '-0.05263157895' to each side of the equation. 0.05263157895 + -0.9473684211x + -0.05263157895 + x2 = 0 + -0.05263157895 Reorder the terms: 0.05263157895 + -0.05263157895 + -0.9473684211x + x2 = 0 + -0.05263157895 Combine like terms: 0.05263157895 + -0.05263157895 = 0.00000000000 0.00000000000 + -0.9473684211x + x2 = 0 + -0.05263157895 -0.9473684211x + x2 = 0 + -0.05263157895 Combine like terms: 0 + -0.05263157895 = -0.05263157895 -0.9473684211x + x2 = -0.05263157895 The x term is -0.9473684211x. Take half its coefficient (-0.4736842106). Square it (0.2243767314) and add it to both sides. Add '0.2243767314' to each side of the equation. -0.9473684211x + 0.2243767314 + x2 = -0.05263157895 + 0.2243767314 Reorder the terms: 0.2243767314 + -0.9473684211x + x2 = -0.05263157895 + 0.2243767314 Combine like terms: -0.05263157895 + 0.2243767314 = 0.17174515245 0.2243767314 + -0.9473684211x + x2 = 0.17174515245 Factor a perfect square on the left side: (x + -0.4736842106)(x + -0.4736842106) = 0.17174515245 Calculate the square root of the right side: 0.414421467 Break this problem into two subproblems by setting (x + -0.4736842106) equal to 0.414421467 and -0.414421467.Subproblem 1
x + -0.4736842106 = 0.414421467 Simplifying x + -0.4736842106 = 0.414421467 Reorder the terms: -0.4736842106 + x = 0.414421467 Solving -0.4736842106 + x = 0.414421467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4736842106' to each side of the equation. -0.4736842106 + 0.4736842106 + x = 0.414421467 + 0.4736842106 Combine like terms: -0.4736842106 + 0.4736842106 = 0.0000000000 0.0000000000 + x = 0.414421467 + 0.4736842106 x = 0.414421467 + 0.4736842106 Combine like terms: 0.414421467 + 0.4736842106 = 0.8881056776 x = 0.8881056776 Simplifying x = 0.8881056776Subproblem 2
x + -0.4736842106 = -0.414421467 Simplifying x + -0.4736842106 = -0.414421467 Reorder the terms: -0.4736842106 + x = -0.414421467 Solving -0.4736842106 + x = -0.414421467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4736842106' to each side of the equation. -0.4736842106 + 0.4736842106 + x = -0.414421467 + 0.4736842106 Combine like terms: -0.4736842106 + 0.4736842106 = 0.0000000000 0.0000000000 + x = -0.414421467 + 0.4736842106 x = -0.414421467 + 0.4736842106 Combine like terms: -0.414421467 + 0.4736842106 = 0.0592627436 x = 0.0592627436 Simplifying x = 0.0592627436Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8881056776, 0.0592627436}
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