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Simplifying 7x3 + -21x2 + 8x = 0 Reorder the terms: 8x + -21x2 + 7x3 = 0 Solving 8x + -21x2 + 7x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(8 + -21x + 7x2) = 0Subproblem 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 '(8 + -21x + 7x2)' equal to zero and attempt to solve: Simplifying 8 + -21x + 7x2 = 0 Solving 8 + -21x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.142857143 + -3x + x2 = 0 Move the constant term to the right: Add '-1.142857143' to each side of the equation. 1.142857143 + -3x + -1.142857143 + x2 = 0 + -1.142857143 Reorder the terms: 1.142857143 + -1.142857143 + -3x + x2 = 0 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + -3x + x2 = 0 + -1.142857143 -3x + x2 = 0 + -1.142857143 Combine like terms: 0 + -1.142857143 = -1.142857143 -3x + x2 = -1.142857143 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -1.142857143 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -1.142857143 + 2.25 Combine like terms: -1.142857143 + 2.25 = 1.107142857 2.25 + -3x + x2 = 1.107142857 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 1.107142857 Calculate the square root of the right side: 1.052208562 Break this problem into two subproblems by setting (x + -1.5) equal to 1.052208562 and -1.052208562.Subproblem 1
x + -1.5 = 1.052208562 Simplifying x + -1.5 = 1.052208562 Reorder the terms: -1.5 + x = 1.052208562 Solving -1.5 + x = 1.052208562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.052208562 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.052208562 + 1.5 x = 1.052208562 + 1.5 Combine like terms: 1.052208562 + 1.5 = 2.552208562 x = 2.552208562 Simplifying x = 2.552208562Subproblem 2
x + -1.5 = -1.052208562 Simplifying x + -1.5 = -1.052208562 Reorder the terms: -1.5 + x = -1.052208562 Solving -1.5 + x = -1.052208562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.052208562 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.052208562 + 1.5 x = -1.052208562 + 1.5 Combine like terms: -1.052208562 + 1.5 = 0.447791438 x = 0.447791438 Simplifying x = 0.447791438Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.552208562, 0.447791438}Solution
x = {0, 2.552208562, 0.447791438}
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