Question

2x(5x-2)+(3x-0.5)*2=2x+3+10x-5+2x+3
Find X
(give step by step)

Answer 1

x = 1.348331477 and 0.148331477

Explanation:

TEPS USING THE QUADRATIC FORMULA2x(5x−2)+(3x−0.5)2=2x+3+10x−5+2x+3Use the distributive property to multiply 2x by 5x−2.10x2−4x+(3x−0.5)×2=2x+3+10x−5+2x+3Use the distributive property to multiply 3x−0.5 by 2.10x2−4x+6x−1=2x+3+10x−5+2x+3Combine −4x and 6x to get 2x.10x2+2x−1=2x+3+10x−5+2x+3Combine 2x and 10x to get 12x.10x2+2x−1=12x+3−5+2x+3 Subtract 5 from 3 to get −2.10x2+2x−1=12x−2+2x+3Combine 12x and 2x to get 14x.10x2+2x−1=14x−2+3Add −2 and 3 to get 1.10x2+2x−1=14x+1Subtract 14x from both sides.10x2+2x−1−14x=1Combine 2x and −14x to get −12x.10x2−12x−1=1Subtract 1 from both sides.10x2−12x−1−1=0Subtract 1 from −1 to get −2.10x2−12x−2=0This equation is in standard form: ax2+bx+c=0. Substitute 10 for a, −12 for b, and −2 for c in the quadratic formula, 2a−b±b2−4ac​​.x=2×10−(−12)±(−12)2−4×10(−2)​​Square −12.x=2×10−(−12)±144−4×10(−2)​​Multiply −4 times 10.x=2×10−(−12)±144−40(−2)​​Multiply −40 times −2.x=2×10−(−12)±144+80​​Add 144 to 80.x=2×10−(−12)±224​​Take the square root of 224.x=2×10−(−12)±414​​The opposite of −12 is 12.x=2×1012±414​​Multiply 2 times 10.x=2012±414​​Now solve the equation x=2012±414​​ when ± is plus. Add 12 to 414​.x=20414​+12​Divide 12+414​ by 20.x=514​+3​Now solve the equation x=2012±414​​ when ± is minus. Subtract 414​from 12.x=2012−414​​Divide 12−414​ by 20.x=53−14​​The equation is now solved.

x=514​+3​x=53−14​​