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Simplifying x = 25x + -2x2 + -50 Reorder the terms: x = -50 + 25x + -2x2 Solving x = -50 + 25x + -2x2 Solving for variable 'x'. Reorder the terms: 50 + x + -25x + 2x2 = -50 + 25x + -2x2 + 50 + -25x + 2x2 Combine like terms: x + -25x = -24x 50 + -24x + 2x2 = -50 + 25x + -2x2 + 50 + -25x + 2x2 Reorder the terms: 50 + -24x + 2x2 = -50 + 50 + 25x + -25x + -2x2 + 2x2 Combine like terms: -50 + 50 = 0 50 + -24x + 2x2 = 0 + 25x + -25x + -2x2 + 2x2 50 + -24x + 2x2 = 25x + -25x + -2x2 + 2x2 Combine like terms: 25x + -25x = 0 50 + -24x + 2x2 = 0 + -2x2 + 2x2 50 + -24x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 50 + -24x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(25 + -12x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(25 + -12x + x2)' equal to zero and attempt to solve: Simplifying 25 + -12x + x2 = 0 Solving 25 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -12x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -12x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -12x + x2 = 0 + -25 -12x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -12x + x2 = -25 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -25 + 36 Reorder the terms: 36 + -12x + x2 = -25 + 36 Combine like terms: -25 + 36 = 11 36 + -12x + x2 = 11 Factor a perfect square on the left side: (x + -6)(x + -6) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + -6) equal to 3.31662479 and -3.31662479.Subproblem 1
x + -6 = 3.31662479 Simplifying x + -6 = 3.31662479 Reorder the terms: -6 + x = 3.31662479 Solving -6 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 3.31662479 + 6 Combine like terms: -6 + 6 = 0 0 + x = 3.31662479 + 6 x = 3.31662479 + 6 Combine like terms: 3.31662479 + 6 = 9.31662479 x = 9.31662479 Simplifying x = 9.31662479Subproblem 2
x + -6 = -3.31662479 Simplifying x + -6 = -3.31662479 Reorder the terms: -6 + x = -3.31662479 Solving -6 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -3.31662479 + 6 Combine like terms: -6 + 6 = 0 0 + x = -3.31662479 + 6 x = -3.31662479 + 6 Combine like terms: -3.31662479 + 6 = 2.68337521 x = 2.68337521 Simplifying x = 2.68337521Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.31662479, 2.68337521}Solution
x = {9.31662479, 2.68337521}
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