X²- 6x = 7 FInd the soultion to the equation by completing the square
2 answers:
Answer:
x = - 1, x = 7
Step-by-step explanation:
Given
x² - 6x = 7
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 3) x + 9 = 7 + 9
(x - 3)² = 16 ( take the square root of both sides )
x - 3 = ± = ± 4
Add 3 to both sides
x = 3 ± 4, that is
x = 3 + 4 = 7 or x = 3 - 4 = - 1
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Answer:
y = x -- 2
Step-by-step explanation
We need to fill out the formula y = mx + b.
First, we must find out what each part of that formula means.
mx = slope
b = y-intercept
y = solution (Always unknown)
We already know the slope of the formula, so we can fill that out.
y = x + b
If it has a slope of -3/2, then that means it is moving down 3 points and moving to the right 2 points to find the next line. because rise over run.
If it passes through the point (-4, 4) then from their subtract 3 to 4, and 2 to -4.
This means the next point it will reach is (-2, 1). Once again, subtract 3 from 1, and add 2 to -2.
The next point it will reach is (0, -2) This gives us the y-intercept of the equation.
Now we can fill out the rest of the formula!
y = x -- 2
Explanation:
6(2x + 5) = 2(3x – 2)
[given]
6(2x) + 6(5) = 2(3x) + 2(-2)
12x + 30 = 6x – 4
[distributive property of equality; individually multiply each addend inside the parenthesis and simplify (distribute the terms) ]
12x + 30 = 6x – 4
–6x –6x
6x + 30 = -4
[subtraction property of equality; subtract both sides by 6x in order to keep the x term on the left side]
6x + 30 = -4
–30 –30
6x = -34
[subtraction property of equality; subtract both sides by 30 in order to keep the constant term on the right side]
6x = -34
÷6 ÷6
x = -34/6
[division property of equality; divide both sides by 6 to eliminate the coefficient of 6 in 6x in order to obtain the variable x]
x = -17/3
[GCF(greatest common factor); divide both sides by the greatest common factor until both numbers are prime (only divisible by 1 and itself]