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Simplifying 0 = 4x3 + 24x2 + -60x Reorder the terms: 0 = -60x + 24x2 + 4x3 Solving 0 = -60x + 24x2 + 4x3 Solving for variable 'x'. Remove the zero: 60x + -24x2 + -4x3 = -60x + 24x2 + 4x3 + 60x + -24x2 + -4x3 Reorder the terms: 60x + -24x2 + -4x3 = -60x + 60x + 24x2 + -24x2 + 4x3 + -4x3 Combine like terms: -60x + 60x = 0 60x + -24x2 + -4x3 = 0 + 24x2 + -24x2 + 4x3 + -4x3 60x + -24x2 + -4x3 = 24x2 + -24x2 + 4x3 + -4x3 Combine like terms: 24x2 + -24x2 = 0 60x + -24x2 + -4x3 = 0 + 4x3 + -4x3 60x + -24x2 + -4x3 = 4x3 + -4x3 Combine like terms: 4x3 + -4x3 = 0 60x + -24x2 + -4x3 = 0 Factor out the Greatest Common Factor (GCF), '4x'. 4x(15 + -6x + -1x2) = 0 Ignore the factor 4.Subproblem 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 '(15 + -6x + -1x2)' equal to zero and attempt to solve: Simplifying 15 + -6x + -1x2 = 0 Solving 15 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -15 + 6x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 6x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 6x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 6x + x2 = 0 + 15 6x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 6x + x2 = 15 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 15 + 9 Reorder the terms: 9 + 6x + x2 = 15 + 9 Combine like terms: 15 + 9 = 24 9 + 6x + x2 = 24 Factor a perfect square on the left side: (x + 3)(x + 3) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (x + 3) equal to 4.898979486 and -4.898979486.Subproblem 1
x + 3 = 4.898979486 Simplifying x + 3 = 4.898979486 Reorder the terms: 3 + x = 4.898979486 Solving 3 + x = 4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 4.898979486 + -3 Combine like terms: 3 + -3 = 0 0 + x = 4.898979486 + -3 x = 4.898979486 + -3 Combine like terms: 4.898979486 + -3 = 1.898979486 x = 1.898979486 Simplifying x = 1.898979486Subproblem 2
x + 3 = -4.898979486 Simplifying x + 3 = -4.898979486 Reorder the terms: 3 + x = -4.898979486 Solving 3 + x = -4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -4.898979486 + -3 Combine like terms: 3 + -3 = 0 0 + x = -4.898979486 + -3 x = -4.898979486 + -3 Combine like terms: -4.898979486 + -3 = -7.898979486 x = -7.898979486 Simplifying x = -7.898979486Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.898979486, -7.898979486}Solution
x = {0, 1.898979486, -7.898979486}
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