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Simplifying 8x3 + -15x2 + 21x + -15x2 + -11x3 = 0 Reorder the terms: 21x + -15x2 + -15x2 + 8x3 + -11x3 = 0 Combine like terms: -15x2 + -15x2 = -30x2 21x + -30x2 + 8x3 + -11x3 = 0 Combine like terms: 8x3 + -11x3 = -3x3 21x + -30x2 + -3x3 = 0 Solving 21x + -30x2 + -3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(7 + -10x + -1x2) = 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 '(7 + -10x + -1x2)' equal to zero and attempt to solve: Simplifying 7 + -10x + -1x2 = 0 Solving 7 + -10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7 + 10x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 10x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 10x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 10x + x2 = 0 + 7 10x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 10x + x2 = 7 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 = 7 + 25 Reorder the terms: 25 + 10x + x2 = 7 + 25 Combine like terms: 7 + 25 = 32 25 + 10x + x2 = 32 Factor a perfect square on the left side: (x + 5)(x + 5) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (x + 5) equal to 5.656854249 and -5.656854249.Subproblem 1
x + 5 = 5.656854249 Simplifying x + 5 = 5.656854249 Reorder the terms: 5 + x = 5.656854249 Solving 5 + x = 5.656854249 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 = 5.656854249 + -5 Combine like terms: 5 + -5 = 0 0 + x = 5.656854249 + -5 x = 5.656854249 + -5 Combine like terms: 5.656854249 + -5 = 0.656854249 x = 0.656854249 Simplifying x = 0.656854249Subproblem 2
x + 5 = -5.656854249 Simplifying x + 5 = -5.656854249 Reorder the terms: 5 + x = -5.656854249 Solving 5 + x = -5.656854249 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 = -5.656854249 + -5 Combine like terms: 5 + -5 = 0 0 + x = -5.656854249 + -5 x = -5.656854249 + -5 Combine like terms: -5.656854249 + -5 = -10.656854249 x = -10.656854249 Simplifying x = -10.656854249Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.656854249, -10.656854249}Solution
x = {0, 0.656854249, -10.656854249}
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