-16x^2+64x+1=29

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Solution for -16x^2+64x+1=29 equation: 


Simplifying
-16x2 + 64x + 1 = 29

Reorder the terms:
1 + 64x + -16x2 = 29

Solving
1 + 64x + -16x2 = 29

Solving for variable 'x'.

Reorder the terms:
1 + -29 + 64x + -16x2 = 29 + -29

Combine like terms: 1 + -29 = -28
-28 + 64x + -16x2 = 29 + -29

Combine like terms: 29 + -29 = 0
-28 + 64x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-7 + 16x + -4x2) = 0

Factor a trinomial.
4((-7 + 2x)(1 + -2x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-7 + 2x)' equal to zero and attempt to solve:

Simplifying
-7 + 2x = 0

Solving
-7 + 2x = 0

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

Add '7' to each side of the equation.
-7 + 7 + 2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 2x = 0 + 7
2x = 0 + 7

Combine like terms: 0 + 7 = 7
2x = 7

Divide each side by '2'.
x = 3.5

Simplifying
x = 3.5

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 = {3.5, 0.5}

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