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Simplifying -6x4 + 42x3 + 30x2 = 0 Reorder the terms: 30x2 + 42x3 + -6x4 = 0 Solving 30x2 + 42x3 + -6x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6x2'. 6x2(5 + 7x + -1x2) = 0 Ignore the factor 6.Subproblem 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 '(5 + 7x + -1x2)' equal to zero and attempt to solve: Simplifying 5 + 7x + -1x2 = 0 Solving 5 + 7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + -7x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -7x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -7x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -7x + x2 = 0 + 5 -7x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -7x + x2 = 5 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 5 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 5 + 12.25 Combine like terms: 5 + 12.25 = 17.25 12.25 + -7x + x2 = 17.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (x + -3.5) equal to 4.153311931 and -4.153311931.Subproblem 1
x + -3.5 = 4.153311931 Simplifying x + -3.5 = 4.153311931 Reorder the terms: -3.5 + x = 4.153311931 Solving -3.5 + x = 4.153311931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 4.153311931 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 4.153311931 + 3.5 x = 4.153311931 + 3.5 Combine like terms: 4.153311931 + 3.5 = 7.653311931 x = 7.653311931 Simplifying x = 7.653311931Subproblem 2
x + -3.5 = -4.153311931 Simplifying x + -3.5 = -4.153311931 Reorder the terms: -3.5 + x = -4.153311931 Solving -3.5 + x = -4.153311931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -4.153311931 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -4.153311931 + 3.5 x = -4.153311931 + 3.5 Combine like terms: -4.153311931 + 3.5 = -0.653311931 x = -0.653311931 Simplifying x = -0.653311931Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.653311931, -0.653311931}Solution
x = {0, 7.653311931, -0.653311931}
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