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Simplifying 60x4 + 70x3 + -10x2 = 0 Reorder the terms: -10x2 + 70x3 + 60x4 = 0 Solving -10x2 + 70x3 + 60x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10x2'. 10x2(-1 + 7x + 6x2) = 0 Ignore the factor 10.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 '(-1 + 7x + 6x2)' equal to zero and attempt to solve: Simplifying -1 + 7x + 6x2 = 0 Solving -1 + 7x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.1666666667 + 1.166666667x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + 1.166666667x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + 1.166666667x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + 1.166666667x + x2 = 0 + 0.1666666667 1.166666667x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 1.166666667x + x2 = 0.1666666667 The x term is 1.166666667x. Take half its coefficient (0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. 1.166666667x + 0.3402777780 + x2 = 0.1666666667 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x + x2 = 0.1666666667 + 0.3402777780 Combine like terms: 0.1666666667 + 0.3402777780 = 0.5069444447 0.3402777780 + 1.166666667x + x2 = 0.5069444447 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = 0.5069444447 Calculate the square root of the right side: 0.712000312 Break this problem into two subproblems by setting (x + 0.5833333335) equal to 0.712000312 and -0.712000312.Subproblem 1
x + 0.5833333335 = 0.712000312 Simplifying x + 0.5833333335 = 0.712000312 Reorder the terms: 0.5833333335 + x = 0.712000312 Solving 0.5833333335 + x = 0.712000312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + x = 0.712000312 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = 0.712000312 + -0.5833333335 x = 0.712000312 + -0.5833333335 Combine like terms: 0.712000312 + -0.5833333335 = 0.1286669785 x = 0.1286669785 Simplifying x = 0.1286669785Subproblem 2
x + 0.5833333335 = -0.712000312 Simplifying x + 0.5833333335 = -0.712000312 Reorder the terms: 0.5833333335 + x = -0.712000312 Solving 0.5833333335 + x = -0.712000312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + x = -0.712000312 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = -0.712000312 + -0.5833333335 x = -0.712000312 + -0.5833333335 Combine like terms: -0.712000312 + -0.5833333335 = -1.2953336455 x = -1.2953336455 Simplifying x = -1.2953336455Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1286669785, -1.2953336455}Solution
x = {0, 0.1286669785, -1.2953336455}
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