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Simplifying 45x2 + -4x3 + -24x4 = 0 Solving 45x2 + -4x3 + -24x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(45 + -4x + -24x2) = 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 '(45 + -4x + -24x2)' equal to zero and attempt to solve: Simplifying 45 + -4x + -24x2 = 0 Solving 45 + -4x + -24x2 = 0 Begin completing the square. Divide all terms by -24 the coefficient of the squared term: Divide each side by '-24'. -1.875 + 0.1666666667x + x2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + 0.1666666667x + 1.875 + x2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + 0.1666666667x + x2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + 0.1666666667x + x2 = 0 + 1.875 0.1666666667x + x2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 0.1666666667x + x2 = 1.875 The x term is 0.1666666667x. Take half its coefficient (0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. 0.1666666667x + 0.006944444447 + x2 = 1.875 + 0.006944444447 Reorder the terms: 0.006944444447 + 0.1666666667x + x2 = 1.875 + 0.006944444447 Combine like terms: 1.875 + 0.006944444447 = 1.881944444447 0.006944444447 + 0.1666666667x + x2 = 1.881944444447 Factor a perfect square on the left side: (x + 0.08333333335)(x + 0.08333333335) = 1.881944444447 Calculate the square root of the right side: 1.371839803 Break this problem into two subproblems by setting (x + 0.08333333335) equal to 1.371839803 and -1.371839803.Subproblem 1
x + 0.08333333335 = 1.371839803 Simplifying x + 0.08333333335 = 1.371839803 Reorder the terms: 0.08333333335 + x = 1.371839803 Solving 0.08333333335 + x = 1.371839803 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + x = 1.371839803 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = 1.371839803 + -0.08333333335 x = 1.371839803 + -0.08333333335 Combine like terms: 1.371839803 + -0.08333333335 = 1.28850646965 x = 1.28850646965 Simplifying x = 1.28850646965Subproblem 2
x + 0.08333333335 = -1.371839803 Simplifying x + 0.08333333335 = -1.371839803 Reorder the terms: 0.08333333335 + x = -1.371839803 Solving 0.08333333335 + x = -1.371839803 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + x = -1.371839803 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = -1.371839803 + -0.08333333335 x = -1.371839803 + -0.08333333335 Combine like terms: -1.371839803 + -0.08333333335 = -1.45517313635 x = -1.45517313635 Simplifying x = -1.45517313635Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.28850646965, -1.45517313635}Solution
x = {0, 1.28850646965, -1.45517313635}
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