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Simplifying 3x3 + 42x2 + -36x = 0 Reorder the terms: -36x + 42x2 + 3x3 = 0 Solving -36x + 42x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(-12 + 14x + x2) = 0 Ignore the factor 3.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 '(-12 + 14x + x2)' equal to zero and attempt to solve: Simplifying -12 + 14x + x2 = 0 Solving -12 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 14x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 14x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 14x + x2 = 0 + 12 14x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 14x + x2 = 12 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 12 + 49 Reorder the terms: 49 + 14x + x2 = 12 + 49 Combine like terms: 12 + 49 = 61 49 + 14x + x2 = 61 Factor a perfect square on the left side: (x + 7)(x + 7) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (x + 7) equal to 7.810249676 and -7.810249676.Subproblem 1
x + 7 = 7.810249676 Simplifying x + 7 = 7.810249676 Reorder the terms: 7 + x = 7.810249676 Solving 7 + x = 7.810249676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 7.810249676 + -7 Combine like terms: 7 + -7 = 0 0 + x = 7.810249676 + -7 x = 7.810249676 + -7 Combine like terms: 7.810249676 + -7 = 0.810249676 x = 0.810249676 Simplifying x = 0.810249676Subproblem 2
x + 7 = -7.810249676 Simplifying x + 7 = -7.810249676 Reorder the terms: 7 + x = -7.810249676 Solving 7 + x = -7.810249676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -7.810249676 + -7 Combine like terms: 7 + -7 = 0 0 + x = -7.810249676 + -7 x = -7.810249676 + -7 Combine like terms: -7.810249676 + -7 = -14.810249676 x = -14.810249676 Simplifying x = -14.810249676Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.810249676, -14.810249676}Solution
x = {0, 0.810249676, -14.810249676}
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