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Simplifying x2 + -28x + -12 = 0 Reorder the terms: -12 + -28x + x2 = 0 Solving -12 + -28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -28x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -28x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -28x + x2 = 0 + 12 -28x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -28x + x2 = 12 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 = 12 + 196 Reorder the terms: 196 + -28x + x2 = 12 + 196 Combine like terms: 12 + 196 = 208 196 + -28x + x2 = 208 Factor a perfect square on the left side: (x + -14)(x + -14) = 208 Calculate the square root of the right side: 14.422205102 Break this problem into two subproblems by setting (x + -14) equal to 14.422205102 and -14.422205102.Subproblem 1
x + -14 = 14.422205102 Simplifying x + -14 = 14.422205102 Reorder the terms: -14 + x = 14.422205102 Solving -14 + x = 14.422205102 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 = 14.422205102 + 14 Combine like terms: -14 + 14 = 0 0 + x = 14.422205102 + 14 x = 14.422205102 + 14 Combine like terms: 14.422205102 + 14 = 28.422205102 x = 28.422205102 Simplifying x = 28.422205102Subproblem 2
x + -14 = -14.422205102 Simplifying x + -14 = -14.422205102 Reorder the terms: -14 + x = -14.422205102 Solving -14 + x = -14.422205102 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 = -14.422205102 + 14 Combine like terms: -14 + 14 = 0 0 + x = -14.422205102 + 14 x = -14.422205102 + 14 Combine like terms: -14.422205102 + 14 = -0.422205102 x = -0.422205102 Simplifying x = -0.422205102Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.422205102, -0.422205102}
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