Solve the equation 2z^2 – 8z +26 = (z + 1)^2?

Answer 1

2z^2 – 8z + 26 = (z + 1)^2
2z^2 – 8z + 26 = z^2 + 2z + 1
z^2 – 10z + 25 = 0
(z – 5)^2 = 0
Only z = 5 will do.

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Answer 2

First: Rewrite the expression on the right without the exponent; then use the foiling method >

2z^2 – 8z +26 = (z + 1)(z + 1)
2z^2 – 8z +26 = z^2 + z + z + 1
2z^2 – 8z +26 = z^2 + 2z + 1

Sec: set the equation to "0" > subtract z^2, subtract 2z, and subtract 1 fom both sides; combine "like" terms; factor the equation >

2z^2 – 8z +26 - z^2 - 2z - 1 = 0
z^2 - 10z + 25 = 0
(z - 5)(z - 5) = 0

Third: since you have two of the same expression, just set one to equal "0" and solve for "z" by adding 5 to both sides >

z - 5 + 5 = 0 + 5
z = 5

Answer 3

2z^2 – 8z +26 = (z + 1)^2
<=> 2z^2 - 8z + 26 = z^2 + 2z +1
<=> z^2 -10z + 25 =0
<=> (z - 5)^2 = 0 <=> z = 5

Answer 4

3y + 2Z = 12 y - z = 9. from the 2d: y = z+9 replace into the 1st 3(z+9) + 2z = 12 3z + 27 + 2z = 12 5z + 27 = 12 subtract 27 from the two aspects 5z = -15 divide by technique of five z = -3 y = z+9 = -3+9 = 6 the respond is C.

Answer 5

Simplifying
2z2 + -8z + 26 = (z + 1)(z + 1)

Reorder the terms:
26 + -8z + 2z2 = (z + 1)(z + 1)

Reorder the terms:
26 + -8z + 2z2 = (1 + z)(z + 1)

Reorder the terms:
26 + -8z + 2z2 = (1 + z)(1 + z)

Multiply (1 + z) * (1 + z)
26 + -8z + 2z2 = (1(1 + z) + z(1 + z))
26 + -8z + 2z2 = ((1 * 1 + z * 1) + z(1 + z))
26 + -8z + 2z2 = ((1 + 1z) + z(1 + z))
26 + -8z + 2z2 = (1 + 1z + (1 * z + z * z))
26 + -8z + 2z2 = (1 + 1z + (1z + z2))

Combine like terms: 1z + 1z = 2z
26 + -8z + 2z2 = (1 + 2z + z2)

Solving
26 + -8z + 2z2 = 1 + 2z + z2

Solving for variable 'z'.

Reorder the terms:
26 + -1 + -8z + -2z + 2z2 + -1z2 = 1 + 2z + z2 + -1 + -2z + -1z2

Combine like terms: 26 + -1 = 25
25 + -8z + -2z + 2z2 + -1z2 = 1 + 2z + z2 + -1 + -2z + -1z2

Combine like terms: -8z + -2z = -10z
25 + -10z + 2z2 + -1z2 = 1 + 2z + z2 + -1 + -2z + -1z2

Combine like terms: 2z2 + -1z2 = 1z2
25 + -10z + 1z2 = 1 + 2z + z2 + -1 + -2z + -1z2

Reorder the terms:
25 + -10z + 1z2 = 1 + -1 + 2z + -2z + z2 + -1z2

Combine like terms: 1 + -1 = 0
25 + -10z + 1z2 = 0 + 2z + -2z + z2 + -1z2
25 + -10z + 1z2 = 2z + -2z + z2 + -1z2

Combine like terms: 2z + -2z = 0
25 + -10z + 1z2 = 0 + z2 + -1z2
25 + -10z + 1z2 = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
25 + -10z + 1z2 = 0

Factor a trinomial.
(5 + -1z)(5 + -1z) = 0

Subproblem 1Set the factor '(5 + -1z)' equal to zero and attempt to solve:

Simplifying
5 + -1z = 0

Solving
5 + -1z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1z = 0 + -5
-1z = 0 + -5

Combine like terms: 0 + -5 = -5
-1z = -5

Divide each side by '-1'.
z = 5

Simplifying
z = 5
Subproblem 2Set the factor '(5 + -1z)' equal to zero and attempt to solve:

Simplifying
5 + -1z = 0

Solving
5 + -1z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1z = 0 + -5
-1z = 0 + -5

Combine like terms: 0 + -5 = -5
-1z = -5

Divide each side by '-1'.
z = 5

Simplifying
z = 5Solutionz = {5, 5}

Answer 6

2z² -8z +26 = (z+1)²

2z² -8z +26 = z² +2z +1

2z² -z² -8z -2z +26 -1 = 0

z² -10z +25 = 0

(z -5) (z -5) = 0

(z -5)² = 0

Therefore, z = 5

Answer 7

2z² – 8z +26 = (z + 1)² INCORRECT!
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Answer 8

Simplify to: z^2-10z+25= 0
Factor: (z-5)^2 = 0
Solve: z = 5