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Simplifying 5x5 + 15x4 + -4x3 = 0 Reorder the terms: -4x3 + 15x4 + 5x5 = 0 Solving -4x3 + 15x4 + 5x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x3'. x3(-4 + 15x + 5x2) = 0Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve: Simplifying x3 = 0 Solving x3 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-4 + 15x + 5x2)' equal to zero and attempt to solve: Simplifying -4 + 15x + 5x2 = 0 Solving -4 + 15x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + 3x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 3x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 3x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 3x + x2 = 0 + 0.8 3x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 3x + x2 = 0.8 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 0.8 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 0.8 + 2.25 Combine like terms: 0.8 + 2.25 = 3.05 2.25 + 3x + x2 = 3.05 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 3.05 Calculate the square root of the right side: 1.74642492 Break this problem into two subproblems by setting (x + 1.5) equal to 1.74642492 and -1.74642492.Subproblem 1
x + 1.5 = 1.74642492 Simplifying x + 1.5 = 1.74642492 Reorder the terms: 1.5 + x = 1.74642492 Solving 1.5 + x = 1.74642492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.74642492 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.74642492 + -1.5 x = 1.74642492 + -1.5 Combine like terms: 1.74642492 + -1.5 = 0.24642492 x = 0.24642492 Simplifying x = 0.24642492Subproblem 2
x + 1.5 = -1.74642492 Simplifying x + 1.5 = -1.74642492 Reorder the terms: 1.5 + x = -1.74642492 Solving 1.5 + x = -1.74642492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.74642492 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.74642492 + -1.5 x = -1.74642492 + -1.5 Combine like terms: -1.74642492 + -1.5 = -3.24642492 x = -3.24642492 Simplifying x = -3.24642492Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.24642492, -3.24642492}Solution
x = {0.24642492, -3.24642492}
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