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Simplifying 5x4 + 16x3 + -48x2 = 0 Reorder the terms: -48x2 + 16x3 + 5x4 = 0 Solving -48x2 + 16x3 + 5x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-48 + 16x + 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 '(-48 + 16x + 5x2)' equal to zero and attempt to solve: Simplifying -48 + 16x + 5x2 = 0 Solving -48 + 16x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -9.6 + 3.2x + x2 = 0 Move the constant term to the right: Add '9.6' to each side of the equation. -9.6 + 3.2x + 9.6 + x2 = 0 + 9.6 Reorder the terms: -9.6 + 9.6 + 3.2x + x2 = 0 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 0.0 + 3.2x + x2 = 0 + 9.6 3.2x + x2 = 0 + 9.6 Combine like terms: 0 + 9.6 = 9.6 3.2x + x2 = 9.6 The x term is 3.2x. Take half its coefficient (1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. 3.2x + 2.56 + x2 = 9.6 + 2.56 Reorder the terms: 2.56 + 3.2x + x2 = 9.6 + 2.56 Combine like terms: 9.6 + 2.56 = 12.16 2.56 + 3.2x + x2 = 12.16 Factor a perfect square on the left side: (x + 1.6)(x + 1.6) = 12.16 Calculate the square root of the right side: 3.487119155 Break this problem into two subproblems by setting (x + 1.6) equal to 3.487119155 and -3.487119155.Subproblem 1
x + 1.6 = 3.487119155 Simplifying x + 1.6 = 3.487119155 Reorder the terms: 1.6 + x = 3.487119155 Solving 1.6 + x = 3.487119155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = 3.487119155 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = 3.487119155 + -1.6 x = 3.487119155 + -1.6 Combine like terms: 3.487119155 + -1.6 = 1.887119155 x = 1.887119155 Simplifying x = 1.887119155Subproblem 2
x + 1.6 = -3.487119155 Simplifying x + 1.6 = -3.487119155 Reorder the terms: 1.6 + x = -3.487119155 Solving 1.6 + x = -3.487119155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = -3.487119155 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = -3.487119155 + -1.6 x = -3.487119155 + -1.6 Combine like terms: -3.487119155 + -1.6 = -5.087119155 x = -5.087119155 Simplifying x = -5.087119155Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.887119155, -5.087119155}Solution
x = {0, 1.887119155, -5.087119155}
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