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Simplifying 3x3 + 21x2 + -75x = 0 Reorder the terms: -75x + 21x2 + 3x3 = 0 Solving -75x + 21x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(-25 + 7x + x2) = 0 Ignore the factor 3.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 '(-25 + 7x + x2)' equal to zero and attempt to solve: Simplifying -25 + 7x + x2 = 0 Solving -25 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 7x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 7x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 7x + x2 = 0 + 25 7x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 7x + x2 = 25 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 25 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 25 + 12.25 Combine like terms: 25 + 12.25 = 37.25 12.25 + 7x + x2 = 37.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 37.25 Calculate the square root of the right side: 6.103277808 Break this problem into two subproblems by setting (x + 3.5) equal to 6.103277808 and -6.103277808.Subproblem 1
x + 3.5 = 6.103277808 Simplifying x + 3.5 = 6.103277808 Reorder the terms: 3.5 + x = 6.103277808 Solving 3.5 + x = 6.103277808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 6.103277808 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 6.103277808 + -3.5 x = 6.103277808 + -3.5 Combine like terms: 6.103277808 + -3.5 = 2.603277808 x = 2.603277808 Simplifying x = 2.603277808Subproblem 2
x + 3.5 = -6.103277808 Simplifying x + 3.5 = -6.103277808 Reorder the terms: 3.5 + x = -6.103277808 Solving 3.5 + x = -6.103277808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -6.103277808 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -6.103277808 + -3.5 x = -6.103277808 + -3.5 Combine like terms: -6.103277808 + -3.5 = -9.603277808 x = -9.603277808 Simplifying x = -9.603277808Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.603277808, -9.603277808}Solution
x = {0, 2.603277808, -9.603277808}
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