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Simplifying 6x2 + 30x + 19 = 0 Reorder the terms: 19 + 30x + 6x2 = 0 Solving 19 + 30x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 3.166666667 + 5x + x2 = 0 Move the constant term to the right: Add '-3.166666667' to each side of the equation. 3.166666667 + 5x + -3.166666667 + x2 = 0 + -3.166666667 Reorder the terms: 3.166666667 + -3.166666667 + 5x + x2 = 0 + -3.166666667 Combine like terms: 3.166666667 + -3.166666667 = 0.000000000 0.000000000 + 5x + x2 = 0 + -3.166666667 5x + x2 = 0 + -3.166666667 Combine like terms: 0 + -3.166666667 = -3.166666667 5x + x2 = -3.166666667 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -3.166666667 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -3.166666667 + 6.25 Combine like terms: -3.166666667 + 6.25 = 3.083333333 6.25 + 5x + x2 = 3.083333333 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 3.083333333 Calculate the square root of the right side: 1.755942292 Break this problem into two subproblems by setting (x + 2.5) equal to 1.755942292 and -1.755942292.Subproblem 1
x + 2.5 = 1.755942292 Simplifying x + 2.5 = 1.755942292 Reorder the terms: 2.5 + x = 1.755942292 Solving 2.5 + x = 1.755942292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 1.755942292 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 1.755942292 + -2.5 x = 1.755942292 + -2.5 Combine like terms: 1.755942292 + -2.5 = -0.744057708 x = -0.744057708 Simplifying x = -0.744057708Subproblem 2
x + 2.5 = -1.755942292 Simplifying x + 2.5 = -1.755942292 Reorder the terms: 2.5 + x = -1.755942292 Solving 2.5 + x = -1.755942292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -1.755942292 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -1.755942292 + -2.5 x = -1.755942292 + -2.5 Combine like terms: -1.755942292 + -2.5 = -4.255942292 x = -4.255942292 Simplifying x = -4.255942292Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.744057708, -4.255942292}
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