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Simplifying 0 = -12x2 + 60x + 2000 Reorder the terms: 0 = 2000 + 60x + -12x2 Solving 0 = 2000 + 60x + -12x2 Solving for variable 'x'. Combine like terms: 0 + -2000 = -2000 -2000 + -60x + 12x2 = 2000 + 60x + -12x2 + -2000 + -60x + 12x2 Reorder the terms: -2000 + -60x + 12x2 = 2000 + -2000 + 60x + -60x + -12x2 + 12x2 Combine like terms: 2000 + -2000 = 0 -2000 + -60x + 12x2 = 0 + 60x + -60x + -12x2 + 12x2 -2000 + -60x + 12x2 = 60x + -60x + -12x2 + 12x2 Combine like terms: 60x + -60x = 0 -2000 + -60x + 12x2 = 0 + -12x2 + 12x2 -2000 + -60x + 12x2 = -12x2 + 12x2 Combine like terms: -12x2 + 12x2 = 0 -2000 + -60x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-500 + -15x + 3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-500 + -15x + 3x2)' equal to zero and attempt to solve: Simplifying -500 + -15x + 3x2 = 0 Solving -500 + -15x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -166.6666667 + -5x + x2 = 0 Move the constant term to the right: Add '166.6666667' to each side of the equation. -166.6666667 + -5x + 166.6666667 + x2 = 0 + 166.6666667 Reorder the terms: -166.6666667 + 166.6666667 + -5x + x2 = 0 + 166.6666667 Combine like terms: -166.6666667 + 166.6666667 = 0.0000000 0.0000000 + -5x + x2 = 0 + 166.6666667 -5x + x2 = 0 + 166.6666667 Combine like terms: 0 + 166.6666667 = 166.6666667 -5x + x2 = 166.6666667 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 166.6666667 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 166.6666667 + 6.25 Combine like terms: 166.6666667 + 6.25 = 172.9166667 6.25 + -5x + x2 = 172.9166667 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 172.9166667 Calculate the square root of the right side: 13.1497782 Break this problem into two subproblems by setting (x + -2.5) equal to 13.1497782 and -13.1497782.Subproblem 1
x + -2.5 = 13.1497782 Simplifying x + -2.5 = 13.1497782 Reorder the terms: -2.5 + x = 13.1497782 Solving -2.5 + x = 13.1497782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 13.1497782 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 13.1497782 + 2.5 x = 13.1497782 + 2.5 Combine like terms: 13.1497782 + 2.5 = 15.6497782 x = 15.6497782 Simplifying x = 15.6497782Subproblem 2
x + -2.5 = -13.1497782 Simplifying x + -2.5 = -13.1497782 Reorder the terms: -2.5 + x = -13.1497782 Solving -2.5 + x = -13.1497782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -13.1497782 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -13.1497782 + 2.5 x = -13.1497782 + 2.5 Combine like terms: -13.1497782 + 2.5 = -10.6497782 x = -10.6497782 Simplifying x = -10.6497782Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.6497782, -10.6497782}Solution
x = {15.6497782, -10.6497782}
| 6t-14=2t-2 | | 5-2/2=4x | | -25p-6(2-5p)=3(p-2)-4 | | 2370=500m+100 | | 4x-3x=6+7x | | 3x^2-4x= | | 349.5=50m+100 | | 349.5=50m+200 | | 3(9x-3)+5x=-5 | | d+5.7=-9.2 | | 2370=500m+225 | | 89x-16=-28+98x | | 2370=500m+200 | | 2370=500m+150 | | 9(-4x+4)=12(3-3x) | | x^2-4x+4=-9 | | -2x+9y=8 | | -16x^2+48=0 | | 349.5=50m+150 | | 6x=5+8 | | 349.5=50m+125 | | -2x+9x=8 | | 6(2x-3)+8=9 | | -10x-12+12x-17=-2 | | 349.5=50m+75 | | 349.5=50m+15 | | -48=-(1-4x)-5(-4x-5) | | -10x-1212x-17=-2 | | y=50m+15 | | x(x+1)=2x(x-6) | | y=(m+8)+5 | | 349.5=50m+25 |