Question

10х^2+29,5х-30=10(х- )(х- )

Answer 1

$\displaystyle\bf\\10x^{2} +29,5x-30=0\\\\D=29,5^{2} -4\cdot 10\cdot (-30)=870,25+1200=2070,25=45,5^{2} \\\\\\x_{1} =\frac{-29,5-45,5}{20} =\frac{-75}{20} =-3,75\\\\\\x_{2} =\frac{-29,5+45,5}{20} =\frac{16}{20} =0,8\\\\\\\boxed{10x^{2} +29,5x-30=10\cdot(x+3,75)\cdot(x-0,8)}$

Answer 2

To factorize the quadratic equation 10x^2 + 29.5x - 30, we can use the product-sum method.

Step 1: Multiply the coefficient of the x^2 term (10) by the constant term (-30). 10 * -30 = -300

Step 2: Find two numbers that multiply to give -300 and add up to the coefficient of the x-term (29.5). The two numbers are 30 and -10, as 30 * -10 = -300 and 30 + (-10) = 20.

Step 3: Rewrite the middle term (29.5x) using the two numbers found in Step 2. 10x^2 + 30x - 10x - 30

Step 4: Group the terms and factor them by pairs. (10x^2 + 30x) - (10x + 30)

Step 5: Factor out the greatest common factor from each pair. 10x(x + 3) - 10(x + 3)

Step 6: Notice that we have a common factor of (x + 3) in both terms. Factor it out. 10(x + 3)(x - 1)

Therefore, the factored form of the equation 10x^2 + 29.5x - 30 = 10(x + 3)(x - 1).