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Simplifying x2 + 28x + 43 = 0 Reorder the terms: 43 + 28x + x2 = 0 Solving 43 + 28x + 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 + 28x + -43 + x2 = 0 + -43 Reorder the terms: 43 + -43 + 28x + x2 = 0 + -43 Combine like terms: 43 + -43 = 0 0 + 28x + x2 = 0 + -43 28x + x2 = 0 + -43 Combine like terms: 0 + -43 = -43 28x + x2 = -43 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = -43 + 196 Reorder the terms: 196 + 28x + x2 = -43 + 196 Combine like terms: -43 + 196 = 153 196 + 28x + x2 = 153 Factor a perfect square on the left side: (x + 14)(x + 14) = 153 Calculate the square root of the right side: 12.369316877 Break this problem into two subproblems by setting (x + 14) equal to 12.369316877 and -12.369316877.Subproblem 1
x + 14 = 12.369316877 Simplifying x + 14 = 12.369316877 Reorder the terms: 14 + x = 12.369316877 Solving 14 + x = 12.369316877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 12.369316877 + -14 Combine like terms: 14 + -14 = 0 0 + x = 12.369316877 + -14 x = 12.369316877 + -14 Combine like terms: 12.369316877 + -14 = -1.630683123 x = -1.630683123 Simplifying x = -1.630683123Subproblem 2
x + 14 = -12.369316877 Simplifying x + 14 = -12.369316877 Reorder the terms: 14 + x = -12.369316877 Solving 14 + x = -12.369316877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -12.369316877 + -14 Combine like terms: 14 + -14 = 0 0 + x = -12.369316877 + -14 x = -12.369316877 + -14 Combine like terms: -12.369316877 + -14 = -26.369316877 x = -26.369316877 Simplifying x = -26.369316877Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.630683123, -26.369316877}
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