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Simplifying 4x3 + -39x2 + 48x2 + -64x = 0 Reorder the terms: -64x + -39x2 + 48x2 + 4x3 = 0 Combine like terms: -39x2 + 48x2 = 9x2 -64x + 9x2 + 4x3 = 0 Solving -64x + 9x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-64 + 9x + 4x2) = 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 '(-64 + 9x + 4x2)' equal to zero and attempt to solve: Simplifying -64 + 9x + 4x2 = 0 Solving -64 + 9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -16 + 2.25x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 2.25x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 2.25x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 2.25x + x2 = 0 + 16 2.25x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 2.25x + x2 = 16 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = 16 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 16 + 1.265625 Combine like terms: 16 + 1.265625 = 17.265625 1.265625 + 2.25x + x2 = 17.265625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 17.265625 Calculate the square root of the right side: 4.155192535 Break this problem into two subproblems by setting (x + 1.125) equal to 4.155192535 and -4.155192535.Subproblem 1
x + 1.125 = 4.155192535 Simplifying x + 1.125 = 4.155192535 Reorder the terms: 1.125 + x = 4.155192535 Solving 1.125 + x = 4.155192535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 4.155192535 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 4.155192535 + -1.125 x = 4.155192535 + -1.125 Combine like terms: 4.155192535 + -1.125 = 3.030192535 x = 3.030192535 Simplifying x = 3.030192535Subproblem 2
x + 1.125 = -4.155192535 Simplifying x + 1.125 = -4.155192535 Reorder the terms: 1.125 + x = -4.155192535 Solving 1.125 + x = -4.155192535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -4.155192535 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -4.155192535 + -1.125 x = -4.155192535 + -1.125 Combine like terms: -4.155192535 + -1.125 = -5.280192535 x = -5.280192535 Simplifying x = -5.280192535Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.030192535, -5.280192535}Solution
x = {0, 3.030192535, -5.280192535}
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