Educational

Solve the Quadratic Equation by Factorization: 6x − 10/x = 27 Question: Solve the following quadratic equation by factorization: $$ 6x-\frac{10}{x}=27 $$ Solution $$ 6x^2-10=27x $$ $$ 6x^2-27x-10=0 $$ $$ 6x^2-30x+3x-10=0 $$ $$ 6x(x-5)+2(x-5)=0 $$ $$ (2x+1)(3x-10)=0 $$ Either $$ 2x+1=0 $$ $$ x=-\frac{1}{2} $$ or $$ 3x-10=0 $$ $$ x=\frac{10}{3} $$ Hence, $$ \boxed{x=-\frac{1}{2},\ […]

Solve the Quadratic Equation by Factorization: 25x(x + 1) = -4 Question: Solve the following quadratic equation by factorization: $$ 25x(x+1)=-4 $$ Solution $$ 25x^2+25x+4=0 $$ $$ 25x^2+20x+5x+4=0 $$ $$ 5x(5x+4)+1(5x+4)=0 $$ $$ (5x+4)(5x+1)=0 $$ Either $$ 5x+4=0 $$ $$ x=-\frac{4}{5} $$ or $$ 5x+1=0 $$ $$ x=-\frac{1}{5} $$ Hence, $$ \boxed{x=-\frac{4}{5},\ -\frac{1}{5}} $$ Next

Solve the Quadratic Equation by Factorization: 3x² = −11x − 10 Question: Solve the following quadratic equation by factorization: $$ 3x^2=-11x-10 $$ Solution $$ 3x^2+11x+10=0 $$ $$ 3x^2+6x+5x+10=0 $$ $$ 3x(x+2)+5(x+2)=0 $$ $$ (x+2)(3x+5)=0 $$ Either $$ x+2=0 $$ $$ x=-2 $$ or $$ 3x+5=0 $$ $$ x=-\frac{5}{3} $$ Hence, $$ \boxed{x=-2,\ -\frac{5}{3}} $$ Next

Solve the Quadratic Equation by Factorization: 48x² − 13x − 1 = 0 Question: Solve the following quadratic equation by factorization: $$ 48x^2-13x-1=0 $$ Solution $$ 48x^2-16x+3x-1=0 $$ $$ 16x(3x-1)+1(3x-1)=0 $$ $$ (3x-1)(16x+1)=0 $$ Either $$ 3x-1=0 $$ $$ x=\frac{1}{3} $$ or $$ 16x+1=0 $$ $$ x=-\frac{1}{16} $$ Hence, $$ \boxed{x=\frac{1}{3},\ -\frac{1}{16}} $$ Next Question

Solve the Quadratic Equation by Factorization: 5x² − 3x − 2 = 0 Question: Solve the following quadratic equation by factorization: $$ 5x^2-3x-2=0 $$ Solution $$ 5x^2-5x+2x-2=0 $$ $$ 5x(x-1)+2(x-1)=0 $$ $$ (x-1)(5x+2)=0 $$ Either $$ x-1=0 $$ $$ x=1 $$ or $$ 5x+2=0 $$ $$ x=-\frac{2}{5} $$ Hence, $$ \boxed{x=1,\ -\frac{2}{5}} $$ Next Question

Solve the Quadratic Equation by Factorization: 6x² + 11x + 3 = 0 Question: Solve the following quadratic equation by factorization: $$ 6x^2+11x+3=0 $$ Solution $$ 6x^2+9x+2x+3=0 $$ $$ 3x(2x+3)+1(2x+3)=0 $$ $$ (2x+3)(3x+1)=0 $$ Either $$ 2x+3=0 $$ $$ x=-\frac{3}{2} $$ or $$ 3x+1=0 $$ $$ x=-\frac{1}{3} $$ Hence, $$ \boxed{x=-\frac{3}{2},\ -\frac{1}{3}} $$ Next Question

Solve the Quadratic Equation by Factorization: 1/(x − 1) − 1/(x + 5) = 6/7 Question: $$ \frac{1}{x-1}-\frac{1}{x+5}=\frac{6}{7}, \quad x\ne1,-5 $$ Solution $$ \frac{(x+5)-(x-1)}{(x-1)(x+5)}=\frac{6}{7} $$ $$ \frac{6}{(x-1)(x+5)}=\frac{6}{7} $$ $$ (x-1)(x+5)=7 $$ $$ x^2+4x-5=7 $$ $$ x^2+4x-12=0 $$ $$ x^2+6x-2x-12=0 $$ $$ x(x+6)-2(x+6)=0 $$ $$ (x+6)(x-2)=0 $$ Either $$ x+6=0 $$ $$ x=-6 $$ or $$

Solve the Quadratic Equation by Factorization: 9x² − 3x − 2 = 0 Question: Solve the following quadratic equation by factorization: $$ 9x^2-3x-2=0 $$ Solution $$ 9x^2-6x+3x-2=0 $$ $$ 3x(3x-2)+1(3x-2)=0 $$ $$ (3x-2)(3x+1)=0 $$ Either $$ 3x-2=0 $$ $$ x=\frac{2}{3} $$ or $$ 3x+1=0 $$ $$ x=-\frac{1}{3} $$ Hence, $$ \boxed{x=\frac{2}{3},\ -\frac{1}{3}} $$ Next Question

Solve the Quadratic Equation by Factorization: 3x² − 14x − 5 = 0 Question: Solve the following quadratic equation by factorization: $$ 3x^2-14x-5=0 $$ Solution $$ 3x^2-15x+x-5=0 $$ $$ 3x(x-5)+1(x-5)=0 $$ $$ (x-5)(3x+1)=0 $$ Either $$ x-5=0 $$ $$ x=5 $$ or $$ 3x+1=0 $$ $$ x=-\frac{1}{3} $$ Hence, $$ \boxed{x=5,\ -\frac{1}{3}} $$ Next Question

Solve the Quadratic Equation by Factorization: (2x + 3)(3x – 7) = 0 Question: Solve the following quadratic equation by factorization: $$ (2x+3)(3x-7)=0 $$ Solution $$ (2x+3)(3x-7)=0 $$ Either $$ 2x+3=0 $$ $$ 2x=-3 $$ $$ x=-\frac{3}{2} $$ or $$ 3x-7=0 $$ $$ 3x=7 $$ $$ x=\frac{7}{3} $$ Hence, $$ \boxed{x=-\frac{3}{2},\ \frac{7}{3}} $$ Next Question