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Simplifying 5x3 + -60x2 + -175x = 0 Reorder the terms: -175x + -60x2 + 5x3 = 0 Solving -175x + -60x2 + 5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x'. 5x(-35 + -12x + x2) = 0 Ignore the factor 5.Subproblem 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 '(-35 + -12x + x2)' equal to zero and attempt to solve: Simplifying -35 + -12x + x2 = 0 Solving -35 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + -12x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + -12x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -12x + x2 = 0 + 35 -12x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 -12x + x2 = 35 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 = 35 + 36 Reorder the terms: 36 + -12x + x2 = 35 + 36 Combine like terms: 35 + 36 = 71 36 + -12x + x2 = 71 Factor a perfect square on the left side: (x + -6)(x + -6) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (x + -6) equal to 8.426149773 and -8.426149773.Subproblem 1
x + -6 = 8.426149773 Simplifying x + -6 = 8.426149773 Reorder the terms: -6 + x = 8.426149773 Solving -6 + x = 8.426149773 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 = 8.426149773 + 6 Combine like terms: -6 + 6 = 0 0 + x = 8.426149773 + 6 x = 8.426149773 + 6 Combine like terms: 8.426149773 + 6 = 14.426149773 x = 14.426149773 Simplifying x = 14.426149773Subproblem 2
x + -6 = -8.426149773 Simplifying x + -6 = -8.426149773 Reorder the terms: -6 + x = -8.426149773 Solving -6 + x = -8.426149773 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 = -8.426149773 + 6 Combine like terms: -6 + 6 = 0 0 + x = -8.426149773 + 6 x = -8.426149773 + 6 Combine like terms: -8.426149773 + 6 = -2.426149773 x = -2.426149773 Simplifying x = -2.426149773Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.426149773, -2.426149773}Solution
x = {0, 14.426149773, -2.426149773}
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