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Simplifying 4x3 + -33x2 + -30x = 0 Reorder the terms: -30x + -33x2 + 4x3 = 0 Solving -30x + -33x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-30 + -33x + 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 '(-30 + -33x + 4x2)' equal to zero and attempt to solve: Simplifying -30 + -33x + 4x2 = 0 Solving -30 + -33x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -7.5 + -8.25x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -8.25x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -8.25x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -8.25x + x2 = 0 + 7.5 -8.25x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -8.25x + x2 = 7.5 The x term is -8.25x. Take half its coefficient (-4.125). Square it (17.015625) and add it to both sides. Add '17.015625' to each side of the equation. -8.25x + 17.015625 + x2 = 7.5 + 17.015625 Reorder the terms: 17.015625 + -8.25x + x2 = 7.5 + 17.015625 Combine like terms: 7.5 + 17.015625 = 24.515625 17.015625 + -8.25x + x2 = 24.515625 Factor a perfect square on the left side: (x + -4.125)(x + -4.125) = 24.515625 Calculate the square root of the right side: 4.95132558 Break this problem into two subproblems by setting (x + -4.125) equal to 4.95132558 and -4.95132558.Subproblem 1
x + -4.125 = 4.95132558 Simplifying x + -4.125 = 4.95132558 Reorder the terms: -4.125 + x = 4.95132558 Solving -4.125 + x = 4.95132558 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.125' to each side of the equation. -4.125 + 4.125 + x = 4.95132558 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + x = 4.95132558 + 4.125 x = 4.95132558 + 4.125 Combine like terms: 4.95132558 + 4.125 = 9.07632558 x = 9.07632558 Simplifying x = 9.07632558Subproblem 2
x + -4.125 = -4.95132558 Simplifying x + -4.125 = -4.95132558 Reorder the terms: -4.125 + x = -4.95132558 Solving -4.125 + x = -4.95132558 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.125' to each side of the equation. -4.125 + 4.125 + x = -4.95132558 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + x = -4.95132558 + 4.125 x = -4.95132558 + 4.125 Combine like terms: -4.95132558 + 4.125 = -0.82632558 x = -0.82632558 Simplifying x = -0.82632558Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.07632558, -0.82632558}Solution
x = {0, 9.07632558, -0.82632558}
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