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Simplifying 56x3 + -170x2 + 98x = 0 Reorder the terms: 98x + -170x2 + 56x3 = 0 Solving 98x + -170x2 + 56x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(49 + -85x + 28x2) = 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 '(49 + -85x + 28x2)' equal to zero and attempt to solve: Simplifying 49 + -85x + 28x2 = 0 Solving 49 + -85x + 28x2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. 1.75 + -3.035714286x + x2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + -3.035714286x + -1.75 + x2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + -3.035714286x + x2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + -3.035714286x + x2 = 0 + -1.75 -3.035714286x + x2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 -3.035714286x + x2 = -1.75 The x term is -3.035714286x. Take half its coefficient (-1.517857143). Square it (2.303890307) and add it to both sides. Add '2.303890307' to each side of the equation. -3.035714286x + 2.303890307 + x2 = -1.75 + 2.303890307 Reorder the terms: 2.303890307 + -3.035714286x + x2 = -1.75 + 2.303890307 Combine like terms: -1.75 + 2.303890307 = 0.553890307 2.303890307 + -3.035714286x + x2 = 0.553890307 Factor a perfect square on the left side: (x + -1.517857143)(x + -1.517857143) = 0.553890307 Calculate the square root of the right side: 0.744238071 Break this problem into two subproblems by setting (x + -1.517857143) equal to 0.744238071 and -0.744238071.Subproblem 1
x + -1.517857143 = 0.744238071 Simplifying x + -1.517857143 = 0.744238071 Reorder the terms: -1.517857143 + x = 0.744238071 Solving -1.517857143 + x = 0.744238071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.517857143' to each side of the equation. -1.517857143 + 1.517857143 + x = 0.744238071 + 1.517857143 Combine like terms: -1.517857143 + 1.517857143 = 0.000000000 0.000000000 + x = 0.744238071 + 1.517857143 x = 0.744238071 + 1.517857143 Combine like terms: 0.744238071 + 1.517857143 = 2.262095214 x = 2.262095214 Simplifying x = 2.262095214Subproblem 2
x + -1.517857143 = -0.744238071 Simplifying x + -1.517857143 = -0.744238071 Reorder the terms: -1.517857143 + x = -0.744238071 Solving -1.517857143 + x = -0.744238071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.517857143' to each side of the equation. -1.517857143 + 1.517857143 + x = -0.744238071 + 1.517857143 Combine like terms: -1.517857143 + 1.517857143 = 0.000000000 0.000000000 + x = -0.744238071 + 1.517857143 x = -0.744238071 + 1.517857143 Combine like terms: -0.744238071 + 1.517857143 = 0.773619072 x = 0.773619072 Simplifying x = 0.773619072Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.262095214, 0.773619072}Solution
x = {0, 2.262095214, 0.773619072}
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