Solve 2(x-5) 3(x-5)=10

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = \frac{15 - 15}{3}, x_{2} = \frac{15 + 15}{3}

Alternative Form

x_{1} \approx 3.709006, x_{2} \approx 6.290994

Evaluate

2 (x - 5) \times 3 (x - 5) = 10

Multiply the terms

More Steps

6 (x - 5)^{2} = 10

Expand the expression

More Steps

6 x^{2} - 60 x + 150 = 10

Move the expression to the left side

6 x^{2} - 60 x + 140 = 0

Substitute a= 6,b= - 60 and c= 140 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{60 \pm ( - 60 ) ^{2} - 4 \times 6 \times 140}{2 \times 6}

Simplify the expression

x = \frac{60 \pm ( - 60 ) ^{2} - 4 \times 6 \times 140}{12}

Simplify the expression

More Steps

x = \frac{60 \pm 240}{12}

Simplify the radical expression

More Steps

x = \frac{60 \pm 4 15}{12}

Separate the equation into 2 possible cases

x = \frac{60 + 4 15}{12} x = \frac{60 - 4 15}{12}

Simplify the expression

More Steps

x = \frac{15 + 15}{3} x = \frac{60 - 4 15}{12}

Simplify the expression

More Steps

x = \frac{15 + 15}{3} x = \frac{15 - 15}{3}

Solution

x_{1} = \frac{15 - 15}{3}, x_{2} = \frac{15 + 15}{3}

Alternative Form

x_{1} \approx 3.709006, x_{2} \approx 6.290994

Show Solution