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Simplifying x2 + 14x + 43 = 0 Reorder the terms: 43 + 14x + x2 = 0 Solving 43 + 14x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-43' to each side of the equation. 43 + 14x + -43 + x2 = 0 + -43 Reorder the terms: 43 + -43 + 14x + x2 = 0 + -43 Combine like terms: 43 + -43 = 0 0 + 14x + x2 = 0 + -43 14x + x2 = 0 + -43 Combine like terms: 0 + -43 = -43 14x + x2 = -43 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 = -43 + 49 Reorder the terms: 49 + 14x + x2 = -43 + 49 Combine like terms: -43 + 49 = 6 49 + 14x + x2 = 6 Factor a perfect square on the left side: (x + 7)(x + 7) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + 7) equal to 2.449489743 and -2.449489743.Subproblem 1
x + 7 = 2.449489743 Simplifying x + 7 = 2.449489743 Reorder the terms: 7 + x = 2.449489743 Solving 7 + x = 2.449489743 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 = 2.449489743 + -7 Combine like terms: 7 + -7 = 0 0 + x = 2.449489743 + -7 x = 2.449489743 + -7 Combine like terms: 2.449489743 + -7 = -4.550510257 x = -4.550510257 Simplifying x = -4.550510257Subproblem 2
x + 7 = -2.449489743 Simplifying x + 7 = -2.449489743 Reorder the terms: 7 + x = -2.449489743 Solving 7 + x = -2.449489743 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 = -2.449489743 + -7 Combine like terms: 7 + -7 = 0 0 + x = -2.449489743 + -7 x = -2.449489743 + -7 Combine like terms: -2.449489743 + -7 = -9.449489743 x = -9.449489743 Simplifying x = -9.449489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.550510257, -9.449489743}
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