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Simplifying 1x2 + 14x + 3 = 0 Reorder the terms: 3 + 14x + 1x2 = 0 Solving 3 + 14x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 14x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 14x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 14x + x2 = 0 + -3 14x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 14x + x2 = -3 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 = -3 + 49 Reorder the terms: 49 + 14x + x2 = -3 + 49 Combine like terms: -3 + 49 = 46 49 + 14x + x2 = 46 Factor a perfect square on the left side: (x + 7)(x + 7) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (x + 7) equal to 6.782329983 and -6.782329983.Subproblem 1
x + 7 = 6.782329983 Simplifying x + 7 = 6.782329983 Reorder the terms: 7 + x = 6.782329983 Solving 7 + x = 6.782329983 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 = 6.782329983 + -7 Combine like terms: 7 + -7 = 0 0 + x = 6.782329983 + -7 x = 6.782329983 + -7 Combine like terms: 6.782329983 + -7 = -0.217670017 x = -0.217670017 Simplifying x = -0.217670017Subproblem 2
x + 7 = -6.782329983 Simplifying x + 7 = -6.782329983 Reorder the terms: 7 + x = -6.782329983 Solving 7 + x = -6.782329983 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 = -6.782329983 + -7 Combine like terms: 7 + -7 = 0 0 + x = -6.782329983 + -7 x = -6.782329983 + -7 Combine like terms: -6.782329983 + -7 = -13.782329983 x = -13.782329983 Simplifying x = -13.782329983Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.217670017, -13.782329983}
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