x+1=(7x+15)(7x+15)

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Solution for x+1=(7x+15)(7x+15) equation:


Simplifying
x + 1 = (7x + 15)(7x + 15)

Reorder the terms:
1 + x = (7x + 15)(7x + 15)

Reorder the terms:
1 + x = (15 + 7x)(7x + 15)

Reorder the terms:
1 + x = (15 + 7x)(15 + 7x)

Multiply (15 + 7x) * (15 + 7x)
1 + x = (15(15 + 7x) + 7x * (15 + 7x))
1 + x = ((15 * 15 + 7x * 15) + 7x * (15 + 7x))
1 + x = ((225 + 105x) + 7x * (15 + 7x))
1 + x = (225 + 105x + (15 * 7x + 7x * 7x))
1 + x = (225 + 105x + (105x + 49x2))

Combine like terms: 105x + 105x = 210x
1 + x = (225 + 210x + 49x2)

Solving
1 + x = 225 + 210x + 49x2

Solving for variable 'x'.

Reorder the terms:
1 + -225 + x + -210x + -49x2 = 225 + 210x + 49x2 + -225 + -210x + -49x2

Combine like terms: 1 + -225 = -224
-224 + x + -210x + -49x2 = 225 + 210x + 49x2 + -225 + -210x + -49x2

Combine like terms: x + -210x = -209x
-224 + -209x + -49x2 = 225 + 210x + 49x2 + -225 + -210x + -49x2

Reorder the terms:
-224 + -209x + -49x2 = 225 + -225 + 210x + -210x + 49x2 + -49x2

Combine like terms: 225 + -225 = 0
-224 + -209x + -49x2 = 0 + 210x + -210x + 49x2 + -49x2
-224 + -209x + -49x2 = 210x + -210x + 49x2 + -49x2

Combine like terms: 210x + -210x = 0
-224 + -209x + -49x2 = 0 + 49x2 + -49x2
-224 + -209x + -49x2 = 49x2 + -49x2

Combine like terms: 49x2 + -49x2 = 0
-224 + -209x + -49x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(224 + 209x + 49x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(224 + 209x + 49x2)' equal to zero and attempt to solve: Simplifying 224 + 209x + 49x2 = 0 Solving 224 + 209x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. 4.571428571 + 4.265306122x + x2 = 0 Move the constant term to the right: Add '-4.571428571' to each side of the equation. 4.571428571 + 4.265306122x + -4.571428571 + x2 = 0 + -4.571428571 Reorder the terms: 4.571428571 + -4.571428571 + 4.265306122x + x2 = 0 + -4.571428571 Combine like terms: 4.571428571 + -4.571428571 = 0.000000000 0.000000000 + 4.265306122x + x2 = 0 + -4.571428571 4.265306122x + x2 = 0 + -4.571428571 Combine like terms: 0 + -4.571428571 = -4.571428571 4.265306122x + x2 = -4.571428571 The x term is 4.265306122x. Take half its coefficient (2.132653061). Square it (4.548209079) and add it to both sides. Add '4.548209079' to each side of the equation. 4.265306122x + 4.548209079 + x2 = -4.571428571 + 4.548209079 Reorder the terms: 4.548209079 + 4.265306122x + x2 = -4.571428571 + 4.548209079 Combine like terms: -4.571428571 + 4.548209079 = -0.023219492 4.548209079 + 4.265306122x + x2 = -0.023219492 Factor a perfect square on the left side: (x + 2.132653061)(x + 2.132653061) = -0.023219492 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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