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Simplifying 6x3 + 9x2 + 12x = 0 Reorder the terms: 12x + 9x2 + 6x3 = 0 Solving 12x + 9x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(4 + 3x + 2x2) = 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 '(4 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying 4 + 3x + 2x2 = 0 Solving 4 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2 + 1.5x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 1.5x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 1.5x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 1.5x + x2 = 0 + -2 1.5x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 1.5x + x2 = -2 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = -2 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -2 + 0.5625 Combine like terms: -2 + 0.5625 = -1.4375 0.5625 + 1.5x + x2 = -1.4375 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -1.4375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
| -2-4-5+h=3h-9 | | 1.33333x+2x=60 | | 12+2w^2-11w=0 | | -9*n-12=8-4*n | | 4V^2-8V+3=0 | | 9a+5a=27 | | 2*3m=11 | | 7*n-4=12-3*n | | 186=6(1-5n) | | k-1=3k-1 | | -8(6n-4)=27 | | 11*n-3=9+5*n | | -2(-4-x)=2x+12 | | 2x+5=4n-7 | | 5n-13=18 | | 3xy+8=4y | | 9+2*n=3*n-2 | | 20-3n=175 | | 5n-13= | | 4(5+7h)=-21 | | 3.9=x-0.39 | | 34=-2+7(b-4) | | 59-4n=911 | | 8v=3(4v+2) | | 3f+5= | | 6x+20=2x+8 | | 59-4n=9 | | 388.72=190+0.72x | | -4+2(1-7z)=33 | | 4x+5(2+4x)=130 | | x-0.39=3.9 | | 5x+43=x+7 |