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Simplifying 9x5 = 35x3 + -4x + 0 Reorder the terms: 9x5 = 0 + -4x + 35x3 Remove the zero: 9x5 = -4x + 35x3 Solving 9x5 = -4x + 35x3 Solving for variable 'x'. Reorder the terms: 4x + -35x3 + 9x5 = -4x + 35x3 + 4x + -35x3 Reorder the terms: 4x + -35x3 + 9x5 = -4x + 4x + 35x3 + -35x3 Combine like terms: -4x + 4x = 0 4x + -35x3 + 9x5 = 0 + 35x3 + -35x3 4x + -35x3 + 9x5 = 35x3 + -35x3 Combine like terms: 35x3 + -35x3 = 0 4x + -35x3 + 9x5 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(4 + -35x2 + 9x4) = 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 + -35x2 + 9x4)' equal to zero and attempt to solve: Simplifying 4 + -35x2 + 9x4 = 0 Solving 4 + -35x2 + 9x4 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.4444444444 + -3.888888889x2 + x4 = 0 Move the constant term to the right: Add '-0.4444444444' to each side of the equation. 0.4444444444 + -3.888888889x2 + -0.4444444444 + x4 = 0 + -0.4444444444 Reorder the terms: 0.4444444444 + -0.4444444444 + -3.888888889x2 + x4 = 0 + -0.4444444444 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 0.0000000000 + -3.888888889x2 + x4 = 0 + -0.4444444444 -3.888888889x2 + x4 = 0 + -0.4444444444 Combine like terms: 0 + -0.4444444444 = -0.4444444444 -3.888888889x2 + x4 = -0.4444444444 The x term is -3.888888889x2. Take half its coefficient (-1.944444445). Square it (3.780864200) and add it to both sides. Add '3.780864200' to each side of the equation. -3.888888889x2 + 3.780864200 + x4 = -0.4444444444 + 3.780864200 Reorder the terms: 3.780864200 + -3.888888889x2 + x4 = -0.4444444444 + 3.780864200 Combine like terms: -0.4444444444 + 3.780864200 = 3.3364197556 3.780864200 + -3.888888889x2 + x4 = 3.3364197556 Factor a perfect square on the left side: (x2 + -1.944444445)(x2 + -1.944444445) = 3.3364197556 Calculate the square root of the right side: 1.826586914 Break this problem into two subproblems by setting (x2 + -1.944444445) equal to 1.826586914 and -1.826586914.Subproblem 1
x2 + -1.944444445 = 1.826586914 Simplifying x2 + -1.944444445 = 1.826586914 Reorder the terms: -1.944444445 + x2 = 1.826586914 Solving -1.944444445 + x2 = 1.826586914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.944444445' to each side of the equation. -1.944444445 + 1.944444445 + x2 = 1.826586914 + 1.944444445 Combine like terms: -1.944444445 + 1.944444445 = 0.000000000 0.000000000 + x2 = 1.826586914 + 1.944444445 x2 = 1.826586914 + 1.944444445 Combine like terms: 1.826586914 + 1.944444445 = 3.771031359 x2 = 3.771031359 Simplifying x2 = 3.771031359 Take the square root of each side: x = {-1.941914354, 1.941914354}Subproblem 2
x2 + -1.944444445 = -1.826586914 Simplifying x2 + -1.944444445 = -1.826586914 Reorder the terms: -1.944444445 + x2 = -1.826586914 Solving -1.944444445 + x2 = -1.826586914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.944444445' to each side of the equation. -1.944444445 + 1.944444445 + x2 = -1.826586914 + 1.944444445 Combine like terms: -1.944444445 + 1.944444445 = 0.000000000 0.000000000 + x2 = -1.826586914 + 1.944444445 x2 = -1.826586914 + 1.944444445 Combine like terms: -1.826586914 + 1.944444445 = 0.117857531 x2 = 0.117857531 Simplifying x2 = 0.117857531 Take the square root of each side: x = {-0.343303846, 0.343303846}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.941914354, 1.941914354, -0.343303846, 0.343303846}Solution
x = {0, -1.941914354, 1.941914354, -0.343303846, 0.343303846}
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