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Simplifying 4x3 + 12x2 + -42x = 0 Reorder the terms: -42x + 12x2 + 4x3 = 0 Solving -42x + 12x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-21 + 6x + 2x2) = 0 Ignore the factor 2.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 '(-21 + 6x + 2x2)' equal to zero and attempt to solve: Simplifying -21 + 6x + 2x2 = 0 Solving -21 + 6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10.5 + 3x + x2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + 3x + 10.5 + x2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + 3x + x2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + 3x + x2 = 0 + 10.5 3x + x2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 3x + x2 = 10.5 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 10.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 10.5 + 2.25 Combine like terms: 10.5 + 2.25 = 12.75 2.25 + 3x + x2 = 12.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 12.75 Calculate the square root of the right side: 3.570714214 Break this problem into two subproblems by setting (x + 1.5) equal to 3.570714214 and -3.570714214.Subproblem 1
x + 1.5 = 3.570714214 Simplifying x + 1.5 = 3.570714214 Reorder the terms: 1.5 + x = 3.570714214 Solving 1.5 + x = 3.570714214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 3.570714214 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.570714214 + -1.5 x = 3.570714214 + -1.5 Combine like terms: 3.570714214 + -1.5 = 2.070714214 x = 2.070714214 Simplifying x = 2.070714214Subproblem 2
x + 1.5 = -3.570714214 Simplifying x + 1.5 = -3.570714214 Reorder the terms: 1.5 + x = -3.570714214 Solving 1.5 + x = -3.570714214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -3.570714214 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.570714214 + -1.5 x = -3.570714214 + -1.5 Combine like terms: -3.570714214 + -1.5 = -5.070714214 x = -5.070714214 Simplifying x = -5.070714214Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.070714214, -5.070714214}Solution
x = {0, 2.070714214, -5.070714214}
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