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Simplifying 5x4 + -9x3 + -3x2 = 0 Reorder the terms: -3x2 + -9x3 + 5x4 = 0 Solving -3x2 + -9x3 + 5x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-3 + -9x + 5x2) = 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 '(-3 + -9x + 5x2)' equal to zero and attempt to solve: Simplifying -3 + -9x + 5x2 = 0 Solving -3 + -9x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + -1.8x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -1.8x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -1.8x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -1.8x + x2 = 0 + 0.6 -1.8x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -1.8x + x2 = 0.6 The x term is -1.8x. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8x + 0.81 + x2 = 0.6 + 0.81 Reorder the terms: 0.81 + -1.8x + x2 = 0.6 + 0.81 Combine like terms: 0.6 + 0.81 = 1.41 0.81 + -1.8x + x2 = 1.41 Factor a perfect square on the left side: (x + -0.9)(x + -0.9) = 1.41 Calculate the square root of the right side: 1.187434209 Break this problem into two subproblems by setting (x + -0.9) equal to 1.187434209 and -1.187434209.Subproblem 1
x + -0.9 = 1.187434209 Simplifying x + -0.9 = 1.187434209 Reorder the terms: -0.9 + x = 1.187434209 Solving -0.9 + x = 1.187434209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = 1.187434209 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 1.187434209 + 0.9 x = 1.187434209 + 0.9 Combine like terms: 1.187434209 + 0.9 = 2.087434209 x = 2.087434209 Simplifying x = 2.087434209Subproblem 2
x + -0.9 = -1.187434209 Simplifying x + -0.9 = -1.187434209 Reorder the terms: -0.9 + x = -1.187434209 Solving -0.9 + x = -1.187434209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = -1.187434209 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = -1.187434209 + 0.9 x = -1.187434209 + 0.9 Combine like terms: -1.187434209 + 0.9 = -0.287434209 x = -0.287434209 Simplifying x = -0.287434209Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.087434209, -0.287434209}Solution
x = {0, 2.087434209, -0.287434209}
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