81x^2+18x+1=x^2+10x+25

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Solution for 81x^2+18x+1=x^2+10x+25 equation:


Simplifying
81x2 + 18x + 1 = x2 + 10x + 25

Reorder the terms:
1 + 18x + 81x2 = x2 + 10x + 25

Reorder the terms:
1 + 18x + 81x2 = 25 + 10x + x2

Solving
1 + 18x + 81x2 = 25 + 10x + x2

Solving for variable 'x'.

Reorder the terms:
1 + -25 + 18x + -10x + 81x2 + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2

Combine like terms: 1 + -25 = -24
-24 + 18x + -10x + 81x2 + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2

Combine like terms: 18x + -10x = 8x
-24 + 8x + 81x2 + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2

Combine like terms: 81x2 + -1x2 = 80x2
-24 + 8x + 80x2 = 25 + 10x + x2 + -25 + -10x + -1x2

Reorder the terms:
-24 + 8x + 80x2 = 25 + -25 + 10x + -10x + x2 + -1x2

Combine like terms: 25 + -25 = 0
-24 + 8x + 80x2 = 0 + 10x + -10x + x2 + -1x2
-24 + 8x + 80x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
-24 + 8x + 80x2 = 0 + x2 + -1x2
-24 + 8x + 80x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-24 + 8x + 80x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-3 + x + 10x2) = 0

Factor a trinomial.
8((-3 + -5x)(1 + -2x)) = 0

Ignore the factor 8.

Subproblem 1

Set the factor '(-3 + -5x)' equal to zero and attempt to solve: Simplifying -3 + -5x = 0 Solving -3 + -5x = 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 + -5x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5x = 0 + 3 -5x = 0 + 3 Combine like terms: 0 + 3 = 3 -5x = 3 Divide each side by '-5'. x = -0.6 Simplifying x = -0.6

Subproblem 2

Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5

Solution

x = {-0.6, 0.5}

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