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Simplifying 0 = 13x2 + -26x + -249.73 Reorder the terms: 0 = -249.73 + -26x + 13x2 Solving 0 = -249.73 + -26x + 13x2 Solving for variable 'x'. Combine like terms: 0 + 249.73 = 249.73 249.73 + 26x + -13x2 = -249.73 + -26x + 13x2 + 249.73 + 26x + -13x2 Reorder the terms: 249.73 + 26x + -13x2 = -249.73 + 249.73 + -26x + 26x + 13x2 + -13x2 Combine like terms: -249.73 + 249.73 = 0.00 249.73 + 26x + -13x2 = 0.00 + -26x + 26x + 13x2 + -13x2 249.73 + 26x + -13x2 = -26x + 26x + 13x2 + -13x2 Combine like terms: -26x + 26x = 0 249.73 + 26x + -13x2 = 0 + 13x2 + -13x2 249.73 + 26x + -13x2 = 13x2 + -13x2 Combine like terms: 13x2 + -13x2 = 0 249.73 + 26x + -13x2 = 0 Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. -19.21 + -2x + x2 = 0 Move the constant term to the right: Add '19.21' to each side of the equation. -19.21 + -2x + 19.21 + x2 = 0 + 19.21 Reorder the terms: -19.21 + 19.21 + -2x + x2 = 0 + 19.21 Combine like terms: -19.21 + 19.21 = 0.00 0.00 + -2x + x2 = 0 + 19.21 -2x + x2 = 0 + 19.21 Combine like terms: 0 + 19.21 = 19.21 -2x + x2 = 19.21 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 19.21 + 1 Reorder the terms: 1 + -2x + x2 = 19.21 + 1 Combine like terms: 19.21 + 1 = 20.21 1 + -2x + x2 = 20.21 Factor a perfect square on the left side: (x + -1)(x + -1) = 20.21 Calculate the square root of the right side: 4.495553359 Break this problem into two subproblems by setting (x + -1) equal to 4.495553359 and -4.495553359.Subproblem 1
x + -1 = 4.495553359 Simplifying x + -1 = 4.495553359 Reorder the terms: -1 + x = 4.495553359 Solving -1 + x = 4.495553359 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 4.495553359 + 1 Combine like terms: -1 + 1 = 0 0 + x = 4.495553359 + 1 x = 4.495553359 + 1 Combine like terms: 4.495553359 + 1 = 5.495553359 x = 5.495553359 Simplifying x = 5.495553359Subproblem 2
x + -1 = -4.495553359 Simplifying x + -1 = -4.495553359 Reorder the terms: -1 + x = -4.495553359 Solving -1 + x = -4.495553359 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -4.495553359 + 1 Combine like terms: -1 + 1 = 0 0 + x = -4.495553359 + 1 x = -4.495553359 + 1 Combine like terms: -4.495553359 + 1 = -3.495553359 x = -3.495553359 Simplifying x = -3.495553359Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.495553359, -3.495553359}
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