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Simplifying 4x3 + 60x2 + 25x = 20x2 Reorder the terms: 25x + 60x2 + 4x3 = 20x2 Solving 25x + 60x2 + 4x3 = 20x2 Solving for variable 'x'. Reorder the terms: 25x + 60x2 + -20x2 + 4x3 = 20x2 + -20x2 Combine like terms: 60x2 + -20x2 = 40x2 25x + 40x2 + 4x3 = 20x2 + -20x2 Combine like terms: 20x2 + -20x2 = 0 25x + 40x2 + 4x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(25 + 40x + 4x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(25 + 40x + 4x2)' equal to zero and attempt to solve: Simplifying 25 + 40x + 4x2 = 0 Solving 25 + 40x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6.25 + 10x + x2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + 10x + -6.25 + x2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + 10x + x2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + 10x + x2 = 0 + -6.25 10x + x2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 10x + x2 = -6.25 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -6.25 + 25 Reorder the terms: 25 + 10x + x2 = -6.25 + 25 Combine like terms: -6.25 + 25 = 18.75 25 + 10x + x2 = 18.75 Factor a perfect square on the left side: (x + 5)(x + 5) = 18.75 Calculate the square root of the right side: 4.330127019 Break this problem into two subproblems by setting (x + 5) equal to 4.330127019 and -4.330127019.Subproblem 1
x + 5 = 4.330127019 Simplifying x + 5 = 4.330127019 Reorder the terms: 5 + x = 4.330127019 Solving 5 + x = 4.330127019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 4.330127019 + -5 Combine like terms: 5 + -5 = 0 0 + x = 4.330127019 + -5 x = 4.330127019 + -5 Combine like terms: 4.330127019 + -5 = -0.669872981 x = -0.669872981 Simplifying x = -0.669872981Subproblem 2
x + 5 = -4.330127019 Simplifying x + 5 = -4.330127019 Reorder the terms: 5 + x = -4.330127019 Solving 5 + x = -4.330127019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -4.330127019 + -5 Combine like terms: 5 + -5 = 0 0 + x = -4.330127019 + -5 x = -4.330127019 + -5 Combine like terms: -4.330127019 + -5 = -9.330127019 x = -9.330127019 Simplifying x = -9.330127019Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.669872981, -9.330127019}Solution
x = {0, -0.669872981, -9.330127019}
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