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Simplifying 4x(3x2 + -7x + -16) = 0 Reorder the terms: 4x(-16 + -7x + 3x2) = 0 (-16 * 4x + -7x * 4x + 3x2 * 4x) = 0 (-64x + -28x2 + 12x3) = 0 Solving -64x + -28x2 + 12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(-16 + -7x + 3x2) = 0 Ignore the factor 4.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 '(-16 + -7x + 3x2)' equal to zero and attempt to solve: Simplifying -16 + -7x + 3x2 = 0 Solving -16 + -7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5.333333333 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + -2.333333333x + 5.333333333 + x2 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + -2.333333333x + x2 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + -2.333333333x + x2 = 0 + 5.333333333 -2.333333333x + x2 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 -2.333333333x + x2 = 5.333333333 The x term is -2.333333333x. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333x + 1.361111112 + x2 = 5.333333333 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = 5.333333333 + 1.361111112 Combine like terms: 5.333333333 + 1.361111112 = 6.694444445 1.361111112 + -2.333333333x + x2 = 6.694444445 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = 6.694444445 Calculate the square root of the right side: 2.587362449 Break this problem into two subproblems by setting (x + -1.166666667) equal to 2.587362449 and -2.587362449.Subproblem 1
x + -1.166666667 = 2.587362449 Simplifying x + -1.166666667 = 2.587362449 Reorder the terms: -1.166666667 + x = 2.587362449 Solving -1.166666667 + x = 2.587362449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = 2.587362449 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 2.587362449 + 1.166666667 x = 2.587362449 + 1.166666667 Combine like terms: 2.587362449 + 1.166666667 = 3.754029116 x = 3.754029116 Simplifying x = 3.754029116Subproblem 2
x + -1.166666667 = -2.587362449 Simplifying x + -1.166666667 = -2.587362449 Reorder the terms: -1.166666667 + x = -2.587362449 Solving -1.166666667 + x = -2.587362449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = -2.587362449 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -2.587362449 + 1.166666667 x = -2.587362449 + 1.166666667 Combine like terms: -2.587362449 + 1.166666667 = -1.420695782 x = -1.420695782 Simplifying x = -1.420695782Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.754029116, -1.420695782}Solution
x = {0, 3.754029116, -1.420695782}
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