Question

Question 8 of
Question 8 (2 points)
What values of x satisfy the equation 2x2 + 3x – 10 = 2x + 5
a
x
=3/2 or x=-5
x=-5/2 or x=2
x=10 or x=-1/2
X=-3 or x=5/2
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Answer 1

Answer:

$x=-3\ or\ \frac{5}{2}$

Step-by-step explanation:

Given:

Given equation is.

$2x^{2} +3x-10=2x+5$

Find values of x?

Solution.

$2x^{2} +3x-10=2x+5$

$2x^{2} +3x-10-2x-5=0$

$2x^{2} +x-15=0$

Find the roots of the equation.

compare the above equation with $ax^{2} +bx+c=0$

Therefore, $a=2,b=1,c=-15$

$x=\frac{-b\pm\sqrt{(b)^{2}-4ac}}{2a}$

Put a,b and c value in above equation.

$x=\frac{-1\pm\sqrt{(1)^{2}-4(2)(-15)}}{2(2)}$

$x=\frac{-1\pm\sqrt{1-8(-15)}}{4}$

$x=\frac{-1\pm\sqrt{1+120}}{4}$

$x=\frac{-1\pm\sqrt{121}}{4}$

$x=\frac{-1\pm\sqrt{(11)^{2}}}{4}$

$x=\frac{-1\pm 11}{4}$

For positive sign

$x=\frac{-1+ 11}{4}$

$x=\frac{10}{4}$

$x=\frac{5}{2}$

For negative sign

$x=\frac{-1- 11}{4}$

$x=\frac{-12}{4}$

$x=-3$

$x=-3\ or\ \frac{5}{2}$

Therefore, the value of $x=-3\ or\ \frac{5}{2}$ satisfy the given equation.