(2x+1)(2x+1)=49

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Solution for (2x+1)(2x+1)=49 equation:


Simplifying
(2x + 1)(2x + 1) = 49

Reorder the terms:
(1 + 2x)(2x + 1) = 49

Reorder the terms:
(1 + 2x)(1 + 2x) = 49

Multiply (1 + 2x) * (1 + 2x)
(1(1 + 2x) + 2x * (1 + 2x)) = 49
((1 * 1 + 2x * 1) + 2x * (1 + 2x)) = 49
((1 + 2x) + 2x * (1 + 2x)) = 49
(1 + 2x + (1 * 2x + 2x * 2x)) = 49
(1 + 2x + (2x + 4x2)) = 49

Combine like terms: 2x + 2x = 4x
(1 + 4x + 4x2) = 49

Solving
1 + 4x + 4x2 = 49

Solving for variable 'x'.

Reorder the terms:
1 + -49 + 4x + 4x2 = 49 + -49

Combine like terms: 1 + -49 = -48
-48 + 4x + 4x2 = 49 + -49

Combine like terms: 49 + -49 = 0
-48 + 4x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-12 + x + x2) = 0

Factor a trinomial.
4((-4 + -1x)(3 + -1x)) = 0

Ignore the factor 4.

Subproblem 1

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

Subproblem 2

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {-4, 3}

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