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Simplifying (5x + 4)(5x + 4) = 81 Reorder the terms: (4 + 5x)(5x + 4) = 81 Reorder the terms: (4 + 5x)(4 + 5x) = 81 Multiply (4 + 5x) * (4 + 5x) (4(4 + 5x) + 5x * (4 + 5x)) = 81 ((4 * 4 + 5x * 4) + 5x * (4 + 5x)) = 81 ((16 + 20x) + 5x * (4 + 5x)) = 81 (16 + 20x + (4 * 5x + 5x * 5x)) = 81 (16 + 20x + (20x + 25x^{2})) = 81 Combine like terms: 20x + 20x = 40x (16 + 40x + 25x^{2}) = 81 Solving 16 + 40x + 25x^{2}= 81 Solving for variable 'x'. Reorder the terms: 16 + -81 + 40x + 25x^{2}= 81 + -81 Combine like terms: 16 + -81 = -65 -65 + 40x + 25x^{2}= 81 + -81 Combine like terms: 81 + -81 = 0 -65 + 40x + 25x^{2}= 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-13 + 8x + 5x^{2}) = 0 Factor a trinomial. 5((-13 + -5x)(1 + -1x)) = 0 Ignore the factor 5.## Subproblem 1

Set the factor '(-13 + -5x)' equal to zero and attempt to solve: Simplifying -13 + -5x = 0 Solving -13 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -5x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -5x = 0 + 13 -5x = 0 + 13 Combine like terms: 0 + 13 = 13 -5x = 13 Divide each side by '-5'. x = -2.6 Simplifying x = -2.6## Subproblem 2

Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1## Solution

x = {-2.6, 1}

| 65=0.2(w-10(4)) | | 2x-3(x+r)=-5 | | 49-14y-y^2=0 | | 65=0.2(w-10e) | | X=3t+4 | | S=0.2(w-10e) | | (x+8)+(13x-7)=15 | | 23x-3=78 | | (2-x)(x^2-9)=0 | | 28x-7=26x-5 | | ln(2x+5)=ln(6x-1) | | 5-3k+7-9k= | | -n^2+12n-63=-4n^2 | | 5r(r-8)=0 | | 49-2=3a-10a | | -4+5y=-14 | | 13x^2-7100x=420000 | | -5-4y=3 | | 13x^2-2900x=210000 | | G+4h=180 | | 4+2(x+10)=50 | | -22=8y+6(y+8) | | 4x^2=-25+20x | | 8-58=-3(-3m)-8(2m)+2m | | -6x+4(x-8)=-20 | | (3+v)(5v+9)=0 | | 55=0.2(285-10e) | | (3.08+x)=3.5 | | 5r^2+7r-5=12 | | 4x+x+10=100 | | (x)=9/x-7 | | 2y/5-3x/4=1/2 | | X^2+34x+156=0 | | 19=5(v+5)-2v | | (x-4y)(4x+3)= | | D=26t^2 | | y=(x+1)(x+4) | | -2x^2+40x-202=0 | | 2x^3-8x^2+30x+16=0 | | 285=0.2(55-10e) | | 12c^2-12d^2=c^2-2cd+d^2 | | 1/2x-10=3/4 | | 3(x^4)=27 | | 3x(x^4)=27 | | (5/8)/(3/14) | | 0.05+0.2x=1.95 | | 0.4x+0.9y=3.6 | | -16=4(x-6)-8x | | 16u^6-10u^4/2u^3 | | 18m-(16mn+14n)= | | (5/8)÷(3/14) | | 2/5c=11 | | -2.5(0)-64=y | | 0/-2cd | | cos(40)=33/x | | v^2+12v-42=3 | | 0-6.1y-4.8=0 | | (Y-k)h=c | | 9.9x-0-4.8=0 | | 9.9x-6.1y-4.8=0 | | 149000=(1/X) | | 1/4v-7/8=-3/2 | | 0=-1w^2+10w | | 5(2x-1)=6(2x+5) | | 12d+15=7d |

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