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Simplifying 5x3 + -14x2 + -6x = 0 Reorder the terms: -6x + -14x2 + 5x3 = 0 Solving -6x + -14x2 + 5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-6 + -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 '(-6 + -14x + 5x2)' equal to zero and attempt to solve: Simplifying -6 + -14x + 5x2 = 0 Solving -6 + -14x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + -2.8x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -2.8x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -2.8x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -2.8x + x2 = 0 + 1.2 -2.8x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -2.8x + x2 = 1.2 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 = 1.2 + 1.96 Reorder the terms: 1.96 + -2.8x + x2 = 1.2 + 1.96 Combine like terms: 1.2 + 1.96 = 3.16 1.96 + -2.8x + x2 = 3.16 Factor a perfect square on the left side: (x + -1.4)(x + -1.4) = 3.16 Calculate the square root of the right side: 1.777638883 Break this problem into two subproblems by setting (x + -1.4) equal to 1.777638883 and -1.777638883.Subproblem 1
x + -1.4 = 1.777638883 Simplifying x + -1.4 = 1.777638883 Reorder the terms: -1.4 + x = 1.777638883 Solving -1.4 + x = 1.777638883 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 = 1.777638883 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = 1.777638883 + 1.4 x = 1.777638883 + 1.4 Combine like terms: 1.777638883 + 1.4 = 3.177638883 x = 3.177638883 Simplifying x = 3.177638883Subproblem 2
x + -1.4 = -1.777638883 Simplifying x + -1.4 = -1.777638883 Reorder the terms: -1.4 + x = -1.777638883 Solving -1.4 + x = -1.777638883 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 = -1.777638883 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = -1.777638883 + 1.4 x = -1.777638883 + 1.4 Combine like terms: -1.777638883 + 1.4 = -0.377638883 x = -0.377638883 Simplifying x = -0.377638883Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.177638883, -0.377638883}Solution
x = {0, 3.177638883, -0.377638883}
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