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Simplifying 19x2 + 39x + 3 = 0 Reorder the terms: 3 + 39x + 19x2 = 0 Solving 3 + 39x + 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'. 0.1578947368 + 2.052631579x + x2 = 0 Move the constant term to the right: Add '-0.1578947368' to each side of the equation. 0.1578947368 + 2.052631579x + -0.1578947368 + x2 = 0 + -0.1578947368 Reorder the terms: 0.1578947368 + -0.1578947368 + 2.052631579x + x2 = 0 + -0.1578947368 Combine like terms: 0.1578947368 + -0.1578947368 = 0.0000000000 0.0000000000 + 2.052631579x + x2 = 0 + -0.1578947368 2.052631579x + x2 = 0 + -0.1578947368 Combine like terms: 0 + -0.1578947368 = -0.1578947368 2.052631579x + x2 = -0.1578947368 The x term is 2.052631579x. Take half its coefficient (1.02631579). Square it (1.053324101) and add it to both sides. Add '1.053324101' to each side of the equation. 2.052631579x + 1.053324101 + x2 = -0.1578947368 + 1.053324101 Reorder the terms: 1.053324101 + 2.052631579x + x2 = -0.1578947368 + 1.053324101 Combine like terms: -0.1578947368 + 1.053324101 = 0.8954293642 1.053324101 + 2.052631579x + x2 = 0.8954293642 Factor a perfect square on the left side: (x + 1.02631579)(x + 1.02631579) = 0.8954293642 Calculate the square root of the right side: 0.946271295 Break this problem into two subproblems by setting (x + 1.02631579) equal to 0.946271295 and -0.946271295.Subproblem 1
x + 1.02631579 = 0.946271295 Simplifying x + 1.02631579 = 0.946271295 Reorder the terms: 1.02631579 + x = 0.946271295 Solving 1.02631579 + x = 0.946271295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.02631579' to each side of the equation. 1.02631579 + -1.02631579 + x = 0.946271295 + -1.02631579 Combine like terms: 1.02631579 + -1.02631579 = 0.00000000 0.00000000 + x = 0.946271295 + -1.02631579 x = 0.946271295 + -1.02631579 Combine like terms: 0.946271295 + -1.02631579 = -0.080044495 x = -0.080044495 Simplifying x = -0.080044495Subproblem 2
x + 1.02631579 = -0.946271295 Simplifying x + 1.02631579 = -0.946271295 Reorder the terms: 1.02631579 + x = -0.946271295 Solving 1.02631579 + x = -0.946271295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.02631579' to each side of the equation. 1.02631579 + -1.02631579 + x = -0.946271295 + -1.02631579 Combine like terms: 1.02631579 + -1.02631579 = 0.00000000 0.00000000 + x = -0.946271295 + -1.02631579 x = -0.946271295 + -1.02631579 Combine like terms: -0.946271295 + -1.02631579 = -1.972587085 x = -1.972587085 Simplifying x = -1.972587085Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.080044495, -1.972587085}
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