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Simplifying 4x3 + 18x2 + -7x = 0 Reorder the terms: -7x + 18x2 + 4x3 = 0 Solving -7x + 18x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-7 + 18x + 4x2) = 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 '(-7 + 18x + 4x2)' equal to zero and attempt to solve: Simplifying -7 + 18x + 4x2 = 0 Solving -7 + 18x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + 4.5x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + 4.5x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + 4.5x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + 4.5x + x2 = 0 + 1.75 4.5x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 4.5x + x2 = 1.75 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 1.75 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 1.75 + 5.0625 Combine like terms: 1.75 + 5.0625 = 6.8125 5.0625 + 4.5x + x2 = 6.8125 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 6.8125 Calculate the square root of the right side: 2.610076627 Break this problem into two subproblems by setting (x + 2.25) equal to 2.610076627 and -2.610076627.Subproblem 1
x + 2.25 = 2.610076627 Simplifying x + 2.25 = 2.610076627 Reorder the terms: 2.25 + x = 2.610076627 Solving 2.25 + x = 2.610076627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 2.610076627 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 2.610076627 + -2.25 x = 2.610076627 + -2.25 Combine like terms: 2.610076627 + -2.25 = 0.360076627 x = 0.360076627 Simplifying x = 0.360076627Subproblem 2
x + 2.25 = -2.610076627 Simplifying x + 2.25 = -2.610076627 Reorder the terms: 2.25 + x = -2.610076627 Solving 2.25 + x = -2.610076627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -2.610076627 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -2.610076627 + -2.25 x = -2.610076627 + -2.25 Combine like terms: -2.610076627 + -2.25 = -4.860076627 x = -4.860076627 Simplifying x = -4.860076627Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.360076627, -4.860076627}Solution
x = {0, 0.360076627, -4.860076627}
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