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Simplifying 5x3 + 14x2 + -57x = 0 Reorder the terms: -57x + 14x2 + 5x3 = 0 Solving -57x + 14x2 + 5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-57 + 14x + 5x2) = 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 '(-57 + 14x + 5x2)' equal to zero and attempt to solve: Simplifying -57 + 14x + 5x2 = 0 Solving -57 + 14x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -11.4 + 2.8x + x2 = 0 Move the constant term to the right: Add '11.4' to each side of the equation. -11.4 + 2.8x + 11.4 + x2 = 0 + 11.4 Reorder the terms: -11.4 + 11.4 + 2.8x + x2 = 0 + 11.4 Combine like terms: -11.4 + 11.4 = 0.0 0.0 + 2.8x + x2 = 0 + 11.4 2.8x + x2 = 0 + 11.4 Combine like terms: 0 + 11.4 = 11.4 2.8x + x2 = 11.4 The x term is 2.8x. Take half its coefficient (1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. 2.8x + 1.96 + x2 = 11.4 + 1.96 Reorder the terms: 1.96 + 2.8x + x2 = 11.4 + 1.96 Combine like terms: 11.4 + 1.96 = 13.36 1.96 + 2.8x + x2 = 13.36 Factor a perfect square on the left side: (x + 1.4)(x + 1.4) = 13.36 Calculate the square root of the right side: 3.655133377 Break this problem into two subproblems by setting (x + 1.4) equal to 3.655133377 and -3.655133377.Subproblem 1
x + 1.4 = 3.655133377 Simplifying x + 1.4 = 3.655133377 Reorder the terms: 1.4 + x = 3.655133377 Solving 1.4 + x = 3.655133377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = 3.655133377 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = 3.655133377 + -1.4 x = 3.655133377 + -1.4 Combine like terms: 3.655133377 + -1.4 = 2.255133377 x = 2.255133377 Simplifying x = 2.255133377Subproblem 2
x + 1.4 = -3.655133377 Simplifying x + 1.4 = -3.655133377 Reorder the terms: 1.4 + x = -3.655133377 Solving 1.4 + x = -3.655133377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = -3.655133377 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = -3.655133377 + -1.4 x = -3.655133377 + -1.4 Combine like terms: -3.655133377 + -1.4 = -5.055133377 x = -5.055133377 Simplifying x = -5.055133377Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.255133377, -5.055133377}Solution
x = {0, 2.255133377, -5.055133377}
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