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Simplifying 2x2 + -28x + -261 = 0 Reorder the terms: -261 + -28x + 2x2 = 0 Solving -261 + -28x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -130.5 + -14x + x2 = 0 Move the constant term to the right: Add '130.5' to each side of the equation. -130.5 + -14x + 130.5 + x2 = 0 + 130.5 Reorder the terms: -130.5 + 130.5 + -14x + x2 = 0 + 130.5 Combine like terms: -130.5 + 130.5 = 0.0 0.0 + -14x + x2 = 0 + 130.5 -14x + x2 = 0 + 130.5 Combine like terms: 0 + 130.5 = 130.5 -14x + x2 = 130.5 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 = 130.5 + 49 Reorder the terms: 49 + -14x + x2 = 130.5 + 49 Combine like terms: 130.5 + 49 = 179.5 49 + -14x + x2 = 179.5 Factor a perfect square on the left side: (x + -7)(x + -7) = 179.5 Calculate the square root of the right side: 13.397761007 Break this problem into two subproblems by setting (x + -7) equal to 13.397761007 and -13.397761007.Subproblem 1
x + -7 = 13.397761007 Simplifying x + -7 = 13.397761007 Reorder the terms: -7 + x = 13.397761007 Solving -7 + x = 13.397761007 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 = 13.397761007 + 7 Combine like terms: -7 + 7 = 0 0 + x = 13.397761007 + 7 x = 13.397761007 + 7 Combine like terms: 13.397761007 + 7 = 20.397761007 x = 20.397761007 Simplifying x = 20.397761007Subproblem 2
x + -7 = -13.397761007 Simplifying x + -7 = -13.397761007 Reorder the terms: -7 + x = -13.397761007 Solving -7 + x = -13.397761007 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 = -13.397761007 + 7 Combine like terms: -7 + 7 = 0 0 + x = -13.397761007 + 7 x = -13.397761007 + 7 Combine like terms: -13.397761007 + 7 = -6.397761007 x = -6.397761007 Simplifying x = -6.397761007Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.397761007, -6.397761007}
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