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Simplifying -13x2 + -5x + -14 + 14x2 + -20x + 8 = 0 Reorder the terms: -14 + 8 + -5x + -20x + -13x2 + 14x2 = 0 Combine like terms: -14 + 8 = -6 -6 + -5x + -20x + -13x2 + 14x2 = 0 Combine like terms: -5x + -20x = -25x -6 + -25x + -13x2 + 14x2 = 0 Combine like terms: -13x2 + 14x2 = 1x2 -6 + -25x + 1x2 = 0 Solving -6 + -25x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -25x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -25x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -25x + x2 = 0 + 6 -25x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -25x + x2 = 6 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = 6 + 156.25 Reorder the terms: 156.25 + -25x + x2 = 6 + 156.25 Combine like terms: 6 + 156.25 = 162.25 156.25 + -25x + x2 = 162.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 162.25 Calculate the square root of the right side: 12.737739203 Break this problem into two subproblems by setting (x + -12.5) equal to 12.737739203 and -12.737739203.Subproblem 1
x + -12.5 = 12.737739203 Simplifying x + -12.5 = 12.737739203 Reorder the terms: -12.5 + x = 12.737739203 Solving -12.5 + x = 12.737739203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 12.737739203 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 12.737739203 + 12.5 x = 12.737739203 + 12.5 Combine like terms: 12.737739203 + 12.5 = 25.237739203 x = 25.237739203 Simplifying x = 25.237739203Subproblem 2
x + -12.5 = -12.737739203 Simplifying x + -12.5 = -12.737739203 Reorder the terms: -12.5 + x = -12.737739203 Solving -12.5 + x = -12.737739203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -12.737739203 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -12.737739203 + 12.5 x = -12.737739203 + 12.5 Combine like terms: -12.737739203 + 12.5 = -0.237739203 x = -0.237739203 Simplifying x = -0.237739203Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.237739203, -0.237739203}
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