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Simplifying x3 + 14x2 + -60x = 0 Reorder the terms: -60x + 14x2 + x3 = 0 Solving -60x + 14x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-60 + 14x + x2) = 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 '(-60 + 14x + x2)' equal to zero and attempt to solve: Simplifying -60 + 14x + x2 = 0 Solving -60 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 14x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + 14x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 14x + x2 = 0 + 60 14x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 14x + x2 = 60 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 60 + 49 Reorder the terms: 49 + 14x + x2 = 60 + 49 Combine like terms: 60 + 49 = 109 49 + 14x + x2 = 109 Factor a perfect square on the left side: (x + 7)(x + 7) = 109 Calculate the square root of the right side: 10.440306509 Break this problem into two subproblems by setting (x + 7) equal to 10.440306509 and -10.440306509.Subproblem 1
x + 7 = 10.440306509 Simplifying x + 7 = 10.440306509 Reorder the terms: 7 + x = 10.440306509 Solving 7 + x = 10.440306509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 10.440306509 + -7 Combine like terms: 7 + -7 = 0 0 + x = 10.440306509 + -7 x = 10.440306509 + -7 Combine like terms: 10.440306509 + -7 = 3.440306509 x = 3.440306509 Simplifying x = 3.440306509Subproblem 2
x + 7 = -10.440306509 Simplifying x + 7 = -10.440306509 Reorder the terms: 7 + x = -10.440306509 Solving 7 + x = -10.440306509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -10.440306509 + -7 Combine like terms: 7 + -7 = 0 0 + x = -10.440306509 + -7 x = -10.440306509 + -7 Combine like terms: -10.440306509 + -7 = -17.440306509 x = -17.440306509 Simplifying x = -17.440306509Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.440306509, -17.440306509}Solution
x = {0, 3.440306509, -17.440306509}
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