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Simplifying 25x4 + -100x3 + -120x2 = 0 Reorder the terms: -120x2 + -100x3 + 25x4 = 0 Solving -120x2 + -100x3 + 25x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x2'. 5x2(-24 + -20x + 5x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-24 + -20x + 5x2)' equal to zero and attempt to solve: Simplifying -24 + -20x + 5x2 = 0 Solving -24 + -20x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.8 + -4x + x2 = 0 Move the constant term to the right: Add '4.8' to each side of the equation. -4.8 + -4x + 4.8 + x2 = 0 + 4.8 Reorder the terms: -4.8 + 4.8 + -4x + x2 = 0 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + -4x + x2 = 0 + 4.8 -4x + x2 = 0 + 4.8 Combine like terms: 0 + 4.8 = 4.8 -4x + x2 = 4.8 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 4.8 + 4 Reorder the terms: 4 + -4x + x2 = 4.8 + 4 Combine like terms: 4.8 + 4 = 8.8 4 + -4x + x2 = 8.8 Factor a perfect square on the left side: (x + -2)(x + -2) = 8.8 Calculate the square root of the right side: 2.966479395 Break this problem into two subproblems by setting (x + -2) equal to 2.966479395 and -2.966479395.Subproblem 1
x + -2 = 2.966479395 Simplifying x + -2 = 2.966479395 Reorder the terms: -2 + x = 2.966479395 Solving -2 + x = 2.966479395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.966479395 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.966479395 + 2 x = 2.966479395 + 2 Combine like terms: 2.966479395 + 2 = 4.966479395 x = 4.966479395 Simplifying x = 4.966479395Subproblem 2
x + -2 = -2.966479395 Simplifying x + -2 = -2.966479395 Reorder the terms: -2 + x = -2.966479395 Solving -2 + x = -2.966479395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.966479395 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.966479395 + 2 x = -2.966479395 + 2 Combine like terms: -2.966479395 + 2 = -0.966479395 x = -0.966479395 Simplifying x = -0.966479395Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.966479395, -0.966479395}Solution
x = {0, 4.966479395, -0.966479395}
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