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Simplifying 4x3 + 27x2 + -35x = 0 Reorder the terms: -35x + 27x2 + 4x3 = 0 Solving -35x + 27x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-35 + 27x + 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 '(-35 + 27x + 4x2)' equal to zero and attempt to solve: Simplifying -35 + 27x + 4x2 = 0 Solving -35 + 27x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -8.75 + 6.75x + x2 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + 6.75x + 8.75 + x2 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + 6.75x + x2 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + 6.75x + x2 = 0 + 8.75 6.75x + x2 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 6.75x + x2 = 8.75 The x term is 6.75x. Take half its coefficient (3.375). Square it (11.390625) and add it to both sides. Add '11.390625' to each side of the equation. 6.75x + 11.390625 + x2 = 8.75 + 11.390625 Reorder the terms: 11.390625 + 6.75x + x2 = 8.75 + 11.390625 Combine like terms: 8.75 + 11.390625 = 20.140625 11.390625 + 6.75x + x2 = 20.140625 Factor a perfect square on the left side: (x + 3.375)(x + 3.375) = 20.140625 Calculate the square root of the right side: 4.487830768 Break this problem into two subproblems by setting (x + 3.375) equal to 4.487830768 and -4.487830768.Subproblem 1
x + 3.375 = 4.487830768 Simplifying x + 3.375 = 4.487830768 Reorder the terms: 3.375 + x = 4.487830768 Solving 3.375 + x = 4.487830768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.375' to each side of the equation. 3.375 + -3.375 + x = 4.487830768 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + x = 4.487830768 + -3.375 x = 4.487830768 + -3.375 Combine like terms: 4.487830768 + -3.375 = 1.112830768 x = 1.112830768 Simplifying x = 1.112830768Subproblem 2
x + 3.375 = -4.487830768 Simplifying x + 3.375 = -4.487830768 Reorder the terms: 3.375 + x = -4.487830768 Solving 3.375 + x = -4.487830768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.375' to each side of the equation. 3.375 + -3.375 + x = -4.487830768 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + x = -4.487830768 + -3.375 x = -4.487830768 + -3.375 Combine like terms: -4.487830768 + -3.375 = -7.862830768 x = -7.862830768 Simplifying x = -7.862830768Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.112830768, -7.862830768}Solution
x = {0, 1.112830768, -7.862830768}
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