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Simplifying 14x3 + 28x2 + -54x = 0 Reorder the terms: -54x + 28x2 + 14x3 = 0 Solving -54x + 28x2 + 14x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-27 + 14x + 7x2) = 0 Ignore the factor 2.Subproblem 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 '(-27 + 14x + 7x2)' equal to zero and attempt to solve: Simplifying -27 + 14x + 7x2 = 0 Solving -27 + 14x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3.857142857 + 2x + x2 = 0 Move the constant term to the right: Add '3.857142857' to each side of the equation. -3.857142857 + 2x + 3.857142857 + x2 = 0 + 3.857142857 Reorder the terms: -3.857142857 + 3.857142857 + 2x + x2 = 0 + 3.857142857 Combine like terms: -3.857142857 + 3.857142857 = 0.000000000 0.000000000 + 2x + x2 = 0 + 3.857142857 2x + x2 = 0 + 3.857142857 Combine like terms: 0 + 3.857142857 = 3.857142857 2x + x2 = 3.857142857 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 3.857142857 + 1 Reorder the terms: 1 + 2x + x2 = 3.857142857 + 1 Combine like terms: 3.857142857 + 1 = 4.857142857 1 + 2x + x2 = 4.857142857 Factor a perfect square on the left side: (x + 1)(x + 1) = 4.857142857 Calculate the square root of the right side: 2.20389266 Break this problem into two subproblems by setting (x + 1) equal to 2.20389266 and -2.20389266.Subproblem 1
x + 1 = 2.20389266 Simplifying x + 1 = 2.20389266 Reorder the terms: 1 + x = 2.20389266 Solving 1 + x = 2.20389266 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.20389266 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.20389266 + -1 x = 2.20389266 + -1 Combine like terms: 2.20389266 + -1 = 1.20389266 x = 1.20389266 Simplifying x = 1.20389266Subproblem 2
x + 1 = -2.20389266 Simplifying x + 1 = -2.20389266 Reorder the terms: 1 + x = -2.20389266 Solving 1 + x = -2.20389266 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.20389266 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.20389266 + -1 x = -2.20389266 + -1 Combine like terms: -2.20389266 + -1 = -3.20389266 x = -3.20389266 Simplifying x = -3.20389266Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.20389266, -3.20389266}Solution
x = {0, 1.20389266, -3.20389266}
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