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Simplifying 2x3 + 7x2 + -36x = 0 Reorder the terms: -36x + 7x2 + 2x3 = 0 Solving -36x + 7x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-36 + 7x + 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 '(-36 + 7x + 2x2)' equal to zero and attempt to solve: Simplifying -36 + 7x + 2x2 = 0 Solving -36 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -18 + 3.5x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + 3.5x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 3.5x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 3.5x + x2 = 0 + 18 3.5x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 3.5x + x2 = 18 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 18 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 18 + 3.0625 Combine like terms: 18 + 3.0625 = 21.0625 3.0625 + 3.5x + x2 = 21.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 21.0625 Calculate the square root of the right side: 4.589389938 Break this problem into two subproblems by setting (x + 1.75) equal to 4.589389938 and -4.589389938.Subproblem 1
x + 1.75 = 4.589389938 Simplifying x + 1.75 = 4.589389938 Reorder the terms: 1.75 + x = 4.589389938 Solving 1.75 + x = 4.589389938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 4.589389938 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 4.589389938 + -1.75 x = 4.589389938 + -1.75 Combine like terms: 4.589389938 + -1.75 = 2.839389938 x = 2.839389938 Simplifying x = 2.839389938Subproblem 2
x + 1.75 = -4.589389938 Simplifying x + 1.75 = -4.589389938 Reorder the terms: 1.75 + x = -4.589389938 Solving 1.75 + x = -4.589389938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -4.589389938 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -4.589389938 + -1.75 x = -4.589389938 + -1.75 Combine like terms: -4.589389938 + -1.75 = -6.339389938 x = -6.339389938 Simplifying x = -6.339389938Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.839389938, -6.339389938}Solution
x = {0, 2.839389938, -6.339389938}
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