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Simplifying 4x4 + 6x3 + -80x2 = 0 Reorder the terms: -80x2 + 6x3 + 4x4 = 0 Solving -80x2 + 6x3 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(-40 + 3x + 2x2) = 0 Ignore the factor 2.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 '(-40 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying -40 + 3x + 2x2 = 0 Solving -40 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -20 + 1.5x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 1.5x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 1.5x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 1.5x + x2 = 0 + 20 1.5x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 1.5x + x2 = 20 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 20 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 20 + 0.5625 Combine like terms: 20 + 0.5625 = 20.5625 0.5625 + 1.5x + x2 = 20.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 20.5625 Calculate the square root of the right side: 4.534589287 Break this problem into two subproblems by setting (x + 0.75) equal to 4.534589287 and -4.534589287.Subproblem 1
x + 0.75 = 4.534589287 Simplifying x + 0.75 = 4.534589287 Reorder the terms: 0.75 + x = 4.534589287 Solving 0.75 + x = 4.534589287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 4.534589287 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 4.534589287 + -0.75 x = 4.534589287 + -0.75 Combine like terms: 4.534589287 + -0.75 = 3.784589287 x = 3.784589287 Simplifying x = 3.784589287Subproblem 2
x + 0.75 = -4.534589287 Simplifying x + 0.75 = -4.534589287 Reorder the terms: 0.75 + x = -4.534589287 Solving 0.75 + x = -4.534589287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -4.534589287 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -4.534589287 + -0.75 x = -4.534589287 + -0.75 Combine like terms: -4.534589287 + -0.75 = -5.284589287 x = -5.284589287 Simplifying x = -5.284589287Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.784589287, -5.284589287}Solution
x = {0, 3.784589287, -5.284589287}
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