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Simplifying 5x3 + 34x2 + -2x = 0 Reorder the terms: -2x + 34x2 + 5x3 = 0 Solving -2x + 34x2 + 5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-2 + 34x + 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 '(-2 + 34x + 5x2)' equal to zero and attempt to solve: Simplifying -2 + 34x + 5x2 = 0 Solving -2 + 34x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + 6.8x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 6.8x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 6.8x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 6.8x + x2 = 0 + 0.4 6.8x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 6.8x + x2 = 0.4 The x term is 6.8x. Take half its coefficient (3.4). Square it (11.56) and add it to both sides. Add '11.56' to each side of the equation. 6.8x + 11.56 + x2 = 0.4 + 11.56 Reorder the terms: 11.56 + 6.8x + x2 = 0.4 + 11.56 Combine like terms: 0.4 + 11.56 = 11.96 11.56 + 6.8x + x2 = 11.96 Factor a perfect square on the left side: (x + 3.4)(x + 3.4) = 11.96 Calculate the square root of the right side: 3.458323293 Break this problem into two subproblems by setting (x + 3.4) equal to 3.458323293 and -3.458323293.Subproblem 1
x + 3.4 = 3.458323293 Simplifying x + 3.4 = 3.458323293 Reorder the terms: 3.4 + x = 3.458323293 Solving 3.4 + x = 3.458323293 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.4' to each side of the equation. 3.4 + -3.4 + x = 3.458323293 + -3.4 Combine like terms: 3.4 + -3.4 = 0.0 0.0 + x = 3.458323293 + -3.4 x = 3.458323293 + -3.4 Combine like terms: 3.458323293 + -3.4 = 0.058323293 x = 0.058323293 Simplifying x = 0.058323293Subproblem 2
x + 3.4 = -3.458323293 Simplifying x + 3.4 = -3.458323293 Reorder the terms: 3.4 + x = -3.458323293 Solving 3.4 + x = -3.458323293 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.4' to each side of the equation. 3.4 + -3.4 + x = -3.458323293 + -3.4 Combine like terms: 3.4 + -3.4 = 0.0 0.0 + x = -3.458323293 + -3.4 x = -3.458323293 + -3.4 Combine like terms: -3.458323293 + -3.4 = -6.858323293 x = -6.858323293 Simplifying x = -6.858323293Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.058323293, -6.858323293}Solution
x = {0, 0.058323293, -6.858323293}
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