(x+1)(x+1)=25

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Solution for (x+1)(x+1)=25 equation:


Simplifying
(x + 1)(x + 1) = 25

Reorder the terms:
(1 + x)(x + 1) = 25

Reorder the terms:
(1 + x)(1 + x) = 25

Multiply (1 + x) * (1 + x)
(1(1 + x) + x(1 + x)) = 25
((1 * 1 + x * 1) + x(1 + x)) = 25
((1 + 1x) + x(1 + x)) = 25
(1 + 1x + (1 * x + x * x)) = 25
(1 + 1x + (1x + x2)) = 25

Combine like terms: 1x + 1x = 2x
(1 + 2x + x2) = 25

Solving
1 + 2x + x2 = 25

Solving for variable 'x'.

Reorder the terms:
1 + -25 + 2x + x2 = 25 + -25

Combine like terms: 1 + -25 = -24
-24 + 2x + x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-24 + 2x + x2 = 0

Factor a trinomial.
(-6 + -1x)(4 + -1x) = 0

Subproblem 1

Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6

Subproblem 2

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Solution

x = {-6, 4}

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