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Simplifying 2x3 + 3x2 + -52x = 0 Reorder the terms: -52x + 3x2 + 2x3 = 0 Solving -52x + 3x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-52 + 3x + 2x2) = 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 '(-52 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying -52 + 3x + 2x2 = 0 Solving -52 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -26 + 1.5x + x2 = 0 Move the constant term to the right: Add '26' to each side of the equation. -26 + 1.5x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + 1.5x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 1.5x + x2 = 0 + 26 1.5x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 1.5x + x2 = 26 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 26 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 26 + 0.5625 Combine like terms: 26 + 0.5625 = 26.5625 0.5625 + 1.5x + x2 = 26.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 26.5625 Calculate the square root of the right side: 5.153882032 Break this problem into two subproblems by setting (x + 0.75) equal to 5.153882032 and -5.153882032.Subproblem 1
x + 0.75 = 5.153882032 Simplifying x + 0.75 = 5.153882032 Reorder the terms: 0.75 + x = 5.153882032 Solving 0.75 + x = 5.153882032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 5.153882032 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 5.153882032 + -0.75 x = 5.153882032 + -0.75 Combine like terms: 5.153882032 + -0.75 = 4.403882032 x = 4.403882032 Simplifying x = 4.403882032Subproblem 2
x + 0.75 = -5.153882032 Simplifying x + 0.75 = -5.153882032 Reorder the terms: 0.75 + x = -5.153882032 Solving 0.75 + x = -5.153882032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -5.153882032 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -5.153882032 + -0.75 x = -5.153882032 + -0.75 Combine like terms: -5.153882032 + -0.75 = -5.903882032 x = -5.903882032 Simplifying x = -5.903882032Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.403882032, -5.903882032}Solution
x = {0, 4.403882032, -5.903882032}
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