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Simplifying -25x(10 + -1x) = 25x + 250 (10 * -25x + -1x * -25x) = 25x + 250 (-250x + 25x2) = 25x + 250 Reorder the terms: -250x + 25x2 = 250 + 25x Solving -250x + 25x2 = 250 + 25x Solving for variable 'x'. Reorder the terms: -250 + -250x + -25x + 25x2 = 250 + 25x + -250 + -25x Combine like terms: -250x + -25x = -275x -250 + -275x + 25x2 = 250 + 25x + -250 + -25x Reorder the terms: -250 + -275x + 25x2 = 250 + -250 + 25x + -25x Combine like terms: 250 + -250 = 0 -250 + -275x + 25x2 = 0 + 25x + -25x -250 + -275x + 25x2 = 25x + -25x Combine like terms: 25x + -25x = 0 -250 + -275x + 25x2 = 0 Factor out the Greatest Common Factor (GCF), '25'. 25(-10 + -11x + x2) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(-10 + -11x + x2)' equal to zero and attempt to solve: Simplifying -10 + -11x + x2 = 0 Solving -10 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -11x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -11x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -11x + x2 = 0 + 10 -11x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -11x + x2 = 10 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 10 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 10 + 30.25 Combine like terms: 10 + 30.25 = 40.25 30.25 + -11x + x2 = 40.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (x + -5.5) equal to 6.34428877 and -6.34428877.Subproblem 1
x + -5.5 = 6.34428877 Simplifying x + -5.5 = 6.34428877 Reorder the terms: -5.5 + x = 6.34428877 Solving -5.5 + x = 6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 6.34428877 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 6.34428877 + 5.5 x = 6.34428877 + 5.5 Combine like terms: 6.34428877 + 5.5 = 11.84428877 x = 11.84428877 Simplifying x = 11.84428877Subproblem 2
x + -5.5 = -6.34428877 Simplifying x + -5.5 = -6.34428877 Reorder the terms: -5.5 + x = -6.34428877 Solving -5.5 + x = -6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -6.34428877 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -6.34428877 + 5.5 x = -6.34428877 + 5.5 Combine like terms: -6.34428877 + 5.5 = -0.84428877 x = -0.84428877 Simplifying x = -0.84428877Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.84428877, -0.84428877}Solution
x = {11.84428877, -0.84428877}
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