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Simplifying -3x4 + 30x3 + -74x2 = 0 Reorder the terms: -74x2 + 30x3 + -3x4 = 0 Solving -74x2 + 30x3 + -3x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-74 + 30x + -3x2) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-74 + 30x + -3x2)' equal to zero and attempt to solve: Simplifying -74 + 30x + -3x2 = 0 Solving -74 + 30x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 24.66666667 + -10x + x2 = 0 Move the constant term to the right: Add '-24.66666667' to each side of the equation. 24.66666667 + -10x + -24.66666667 + x2 = 0 + -24.66666667 Reorder the terms: 24.66666667 + -24.66666667 + -10x + x2 = 0 + -24.66666667 Combine like terms: 24.66666667 + -24.66666667 = 0.00000000 0.00000000 + -10x + x2 = 0 + -24.66666667 -10x + x2 = 0 + -24.66666667 Combine like terms: 0 + -24.66666667 = -24.66666667 -10x + x2 = -24.66666667 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 = -24.66666667 + 25 Reorder the terms: 25 + -10x + x2 = -24.66666667 + 25 Combine like terms: -24.66666667 + 25 = 0.33333333 25 + -10x + x2 = 0.33333333 Factor a perfect square on the left side: (x + -5)(x + -5) = 0.33333333 Calculate the square root of the right side: 0.577350266 Break this problem into two subproblems by setting (x + -5) equal to 0.577350266 and -0.577350266.Subproblem 1
x + -5 = 0.577350266 Simplifying x + -5 = 0.577350266 Reorder the terms: -5 + x = 0.577350266 Solving -5 + x = 0.577350266 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 = 0.577350266 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0.577350266 + 5 x = 0.577350266 + 5 Combine like terms: 0.577350266 + 5 = 5.577350266 x = 5.577350266 Simplifying x = 5.577350266Subproblem 2
x + -5 = -0.577350266 Simplifying x + -5 = -0.577350266 Reorder the terms: -5 + x = -0.577350266 Solving -5 + x = -0.577350266 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 = -0.577350266 + 5 Combine like terms: -5 + 5 = 0 0 + x = -0.577350266 + 5 x = -0.577350266 + 5 Combine like terms: -0.577350266 + 5 = 4.422649734 x = 4.422649734 Simplifying x = 4.422649734Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.577350266, 4.422649734}Solution
x = {0, 5.577350266, 4.422649734}
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