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Simplifying -72x4 + -45x3 + 63x2 = 0 Reorder the terms: 63x2 + -45x3 + -72x4 = 0 Solving 63x2 + -45x3 + -72x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9x2'. 9x2(7 + -5x + -8x2) = 0 Ignore the factor 9.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 '(7 + -5x + -8x2)' equal to zero and attempt to solve: Simplifying 7 + -5x + -8x2 = 0 Solving 7 + -5x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.875 + 0.625x + x2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + 0.625x + 0.875 + x2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + 0.625x + x2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + 0.625x + x2 = 0 + 0.875 0.625x + x2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 0.625x + x2 = 0.875 The x term is 0.625x. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625x + 0.09765625 + x2 = 0.875 + 0.09765625 Reorder the terms: 0.09765625 + 0.625x + x2 = 0.875 + 0.09765625 Combine like terms: 0.875 + 0.09765625 = 0.97265625 0.09765625 + 0.625x + x2 = 0.97265625 Factor a perfect square on the left side: (x + 0.3125)(x + 0.3125) = 0.97265625 Calculate the square root of the right side: 0.986233365 Break this problem into two subproblems by setting (x + 0.3125) equal to 0.986233365 and -0.986233365.Subproblem 1
x + 0.3125 = 0.986233365 Simplifying x + 0.3125 = 0.986233365 Reorder the terms: 0.3125 + x = 0.986233365 Solving 0.3125 + x = 0.986233365 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + x = 0.986233365 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x = 0.986233365 + -0.3125 x = 0.986233365 + -0.3125 Combine like terms: 0.986233365 + -0.3125 = 0.673733365 x = 0.673733365 Simplifying x = 0.673733365Subproblem 2
x + 0.3125 = -0.986233365 Simplifying x + 0.3125 = -0.986233365 Reorder the terms: 0.3125 + x = -0.986233365 Solving 0.3125 + x = -0.986233365 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + x = -0.986233365 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x = -0.986233365 + -0.3125 x = -0.986233365 + -0.3125 Combine like terms: -0.986233365 + -0.3125 = -1.298733365 x = -1.298733365 Simplifying x = -1.298733365Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.673733365, -1.298733365}Solution
x = {0, 0.673733365, -1.298733365}
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