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Simplifying 3x2 + 42x + -19 = 0 Reorder the terms: -19 + 42x + 3x2 = 0 Solving -19 + 42x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6.333333333 + 14x + x2 = 0 Move the constant term to the right: Add '6.333333333' to each side of the equation. -6.333333333 + 14x + 6.333333333 + x2 = 0 + 6.333333333 Reorder the terms: -6.333333333 + 6.333333333 + 14x + x2 = 0 + 6.333333333 Combine like terms: -6.333333333 + 6.333333333 = 0.000000000 0.000000000 + 14x + x2 = 0 + 6.333333333 14x + x2 = 0 + 6.333333333 Combine like terms: 0 + 6.333333333 = 6.333333333 14x + x2 = 6.333333333 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 6.333333333 + 49 Reorder the terms: 49 + 14x + x2 = 6.333333333 + 49 Combine like terms: 6.333333333 + 49 = 55.333333333 49 + 14x + x2 = 55.333333333 Factor a perfect square on the left side: (x + 7)(x + 7) = 55.333333333 Calculate the square root of the right side: 7.438637868 Break this problem into two subproblems by setting (x + 7) equal to 7.438637868 and -7.438637868.Subproblem 1
x + 7 = 7.438637868 Simplifying x + 7 = 7.438637868 Reorder the terms: 7 + x = 7.438637868 Solving 7 + x = 7.438637868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 7.438637868 + -7 Combine like terms: 7 + -7 = 0 0 + x = 7.438637868 + -7 x = 7.438637868 + -7 Combine like terms: 7.438637868 + -7 = 0.438637868 x = 0.438637868 Simplifying x = 0.438637868Subproblem 2
x + 7 = -7.438637868 Simplifying x + 7 = -7.438637868 Reorder the terms: 7 + x = -7.438637868 Solving 7 + x = -7.438637868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -7.438637868 + -7 Combine like terms: 7 + -7 = 0 0 + x = -7.438637868 + -7 x = -7.438637868 + -7 Combine like terms: -7.438637868 + -7 = -14.438637868 x = -14.438637868 Simplifying x = -14.438637868Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.438637868, -14.438637868}
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