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Simplifying 8x3 + -30x2 + -504x = 0 Reorder the terms: -504x + -30x2 + 8x3 = 0 Solving -504x + -30x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-252 + -15x + 4x2) = 0 Ignore the factor 2.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 '(-252 + -15x + 4x2)' equal to zero and attempt to solve: Simplifying -252 + -15x + 4x2 = 0 Solving -252 + -15x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -63 + -3.75x + x2 = 0 Move the constant term to the right: Add '63' to each side of the equation. -63 + -3.75x + 63 + x2 = 0 + 63 Reorder the terms: -63 + 63 + -3.75x + x2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + -3.75x + x2 = 0 + 63 -3.75x + x2 = 0 + 63 Combine like terms: 0 + 63 = 63 -3.75x + x2 = 63 The x term is -3.75x. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75x + 3.515625 + x2 = 63 + 3.515625 Reorder the terms: 3.515625 + -3.75x + x2 = 63 + 3.515625 Combine like terms: 63 + 3.515625 = 66.515625 3.515625 + -3.75x + x2 = 66.515625 Factor a perfect square on the left side: (x + -1.875)(x + -1.875) = 66.515625 Calculate the square root of the right side: 8.155711189 Break this problem into two subproblems by setting (x + -1.875) equal to 8.155711189 and -8.155711189.Subproblem 1
x + -1.875 = 8.155711189 Simplifying x + -1.875 = 8.155711189 Reorder the terms: -1.875 + x = 8.155711189 Solving -1.875 + x = 8.155711189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = 8.155711189 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 8.155711189 + 1.875 x = 8.155711189 + 1.875 Combine like terms: 8.155711189 + 1.875 = 10.030711189 x = 10.030711189 Simplifying x = 10.030711189Subproblem 2
x + -1.875 = -8.155711189 Simplifying x + -1.875 = -8.155711189 Reorder the terms: -1.875 + x = -8.155711189 Solving -1.875 + x = -8.155711189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = -8.155711189 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -8.155711189 + 1.875 x = -8.155711189 + 1.875 Combine like terms: -8.155711189 + 1.875 = -6.280711189 x = -6.280711189 Simplifying x = -6.280711189Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.030711189, -6.280711189}Solution
x = {0, 10.030711189, -6.280711189}
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