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Simplifying 7x5 + -98x3 + 4x = 0 Reorder the terms: 4x + -98x3 + 7x5 = 0 Solving 4x + -98x3 + 7x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(4 + -98x2 + 7x4) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(4 + -98x2 + 7x4)' equal to zero and attempt to solve: Simplifying 4 + -98x2 + 7x4 = 0 Solving 4 + -98x2 + 7x4 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.5714285714 + -14x2 + x4 = 0 Move the constant term to the right: Add '-0.5714285714' to each side of the equation. 0.5714285714 + -14x2 + -0.5714285714 + x4 = 0 + -0.5714285714 Reorder the terms: 0.5714285714 + -0.5714285714 + -14x2 + x4 = 0 + -0.5714285714 Combine like terms: 0.5714285714 + -0.5714285714 = 0.0000000000 0.0000000000 + -14x2 + x4 = 0 + -0.5714285714 -14x2 + x4 = 0 + -0.5714285714 Combine like terms: 0 + -0.5714285714 = -0.5714285714 -14x2 + x4 = -0.5714285714 The x term is -14x2. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x2 + 49 + x4 = -0.5714285714 + 49 Reorder the terms: 49 + -14x2 + x4 = -0.5714285714 + 49 Combine like terms: -0.5714285714 + 49 = 48.4285714286 49 + -14x2 + x4 = 48.4285714286 Factor a perfect square on the left side: (x2 + -7)(x2 + -7) = 48.4285714286 Calculate the square root of the right side: 6.959063976 Break this problem into two subproblems by setting (x2 + -7) equal to 6.959063976 and -6.959063976.Subproblem 1
x2 + -7 = 6.959063976 Simplifying x2 + -7 = 6.959063976 Reorder the terms: -7 + x2 = 6.959063976 Solving -7 + x2 = 6.959063976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x2 = 6.959063976 + 7 Combine like terms: -7 + 7 = 0 0 + x2 = 6.959063976 + 7 x2 = 6.959063976 + 7 Combine like terms: 6.959063976 + 7 = 13.959063976 x2 = 13.959063976 Simplifying x2 = 13.959063976 Take the square root of each side: x = {-3.736183076, 3.736183076}Subproblem 2
x2 + -7 = -6.959063976 Simplifying x2 + -7 = -6.959063976 Reorder the terms: -7 + x2 = -6.959063976 Solving -7 + x2 = -6.959063976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x2 = -6.959063976 + 7 Combine like terms: -7 + 7 = 0 0 + x2 = -6.959063976 + 7 x2 = -6.959063976 + 7 Combine like terms: -6.959063976 + 7 = 0.040936024 x2 = 0.040936024 Simplifying x2 = 0.040936024 Take the square root of each side: x = {-0.202326528, 0.202326528}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.736183076, 3.736183076, -0.202326528, 0.202326528}Solution
x = {0, -3.736183076, 3.736183076, -0.202326528, 0.202326528}
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