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Simplifying 10x4 + -39x3 + 11x2 = 0 Reorder the terms: 11x2 + -39x3 + 10x4 = 0 Solving 11x2 + -39x3 + 10x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(11 + -39x + 10x2) = 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 '(11 + -39x + 10x2)' equal to zero and attempt to solve: Simplifying 11 + -39x + 10x2 = 0 Solving 11 + -39x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1.1 + -3.9x + x2 = 0 Move the constant term to the right: Add '-1.1' to each side of the equation. 1.1 + -3.9x + -1.1 + x2 = 0 + -1.1 Reorder the terms: 1.1 + -1.1 + -3.9x + x2 = 0 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + -3.9x + x2 = 0 + -1.1 -3.9x + x2 = 0 + -1.1 Combine like terms: 0 + -1.1 = -1.1 -3.9x + x2 = -1.1 The x term is -3.9x. Take half its coefficient (-1.95). Square it (3.8025) and add it to both sides. Add '3.8025' to each side of the equation. -3.9x + 3.8025 + x2 = -1.1 + 3.8025 Reorder the terms: 3.8025 + -3.9x + x2 = -1.1 + 3.8025 Combine like terms: -1.1 + 3.8025 = 2.7025 3.8025 + -3.9x + x2 = 2.7025 Factor a perfect square on the left side: (x + -1.95)(x + -1.95) = 2.7025 Calculate the square root of the right side: 1.643928222 Break this problem into two subproblems by setting (x + -1.95) equal to 1.643928222 and -1.643928222.Subproblem 1
x + -1.95 = 1.643928222 Simplifying x + -1.95 = 1.643928222 Reorder the terms: -1.95 + x = 1.643928222 Solving -1.95 + x = 1.643928222 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.95' to each side of the equation. -1.95 + 1.95 + x = 1.643928222 + 1.95 Combine like terms: -1.95 + 1.95 = 0.00 0.00 + x = 1.643928222 + 1.95 x = 1.643928222 + 1.95 Combine like terms: 1.643928222 + 1.95 = 3.593928222 x = 3.593928222 Simplifying x = 3.593928222Subproblem 2
x + -1.95 = -1.643928222 Simplifying x + -1.95 = -1.643928222 Reorder the terms: -1.95 + x = -1.643928222 Solving -1.95 + x = -1.643928222 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.95' to each side of the equation. -1.95 + 1.95 + x = -1.643928222 + 1.95 Combine like terms: -1.95 + 1.95 = 0.00 0.00 + x = -1.643928222 + 1.95 x = -1.643928222 + 1.95 Combine like terms: -1.643928222 + 1.95 = 0.306071778 x = 0.306071778 Simplifying x = 0.306071778Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.593928222, 0.306071778}Solution
x = {0, 3.593928222, 0.306071778}
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