26=2(4x-1)2(x+4)

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Solution for 26=2(4x-1)2(x+4) equation:


Simplifying
26 = 2(4x + -1) * 2(x + 4)

Reorder the terms:
26 = 2(-1 + 4x) * 2(x + 4)

Reorder the terms:
26 = 2(-1 + 4x) * 2(4 + x)

Reorder the terms for easier multiplication:
26 = 2 * 2(-1 + 4x)(4 + x)

Multiply 2 * 2
26 = 4(-1 + 4x)(4 + x)

Multiply (-1 + 4x) * (4 + x)
26 = 4(-1(4 + x) + 4x * (4 + x))
26 = 4((4 * -1 + x * -1) + 4x * (4 + x))
26 = 4((-4 + -1x) + 4x * (4 + x))
26 = 4(-4 + -1x + (4 * 4x + x * 4x))
26 = 4(-4 + -1x + (16x + 4x2))

Combine like terms: -1x + 16x = 15x
26 = 4(-4 + 15x + 4x2)
26 = (-4 * 4 + 15x * 4 + 4x2 * 4)
26 = (-16 + 60x + 16x2)

Solving
26 = -16 + 60x + 16x2

Solving for variable 'x'.

Combine like terms: 26 + 16 = 42
42 + -60x + -16x2 = -16 + 60x + 16x2 + 16 + -60x + -16x2

Reorder the terms:
42 + -60x + -16x2 = -16 + 16 + 60x + -60x + 16x2 + -16x2

Combine like terms: -16 + 16 = 0
42 + -60x + -16x2 = 0 + 60x + -60x + 16x2 + -16x2
42 + -60x + -16x2 = 60x + -60x + 16x2 + -16x2

Combine like terms: 60x + -60x = 0
42 + -60x + -16x2 = 0 + 16x2 + -16x2
42 + -60x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
42 + -60x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + -30x + -8x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(21 + -30x + -8x2)' equal to zero and attempt to solve: Simplifying 21 + -30x + -8x2 = 0 Solving 21 + -30x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -2.625 + 3.75x + x2 = 0 Move the constant term to the right: Add '2.625' to each side of the equation. -2.625 + 3.75x + 2.625 + x2 = 0 + 2.625 Reorder the terms: -2.625 + 2.625 + 3.75x + x2 = 0 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + 3.75x + x2 = 0 + 2.625 3.75x + x2 = 0 + 2.625 Combine like terms: 0 + 2.625 = 2.625 3.75x + x2 = 2.625 The x term is 3.75x. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75x + 3.515625 + x2 = 2.625 + 3.515625 Reorder the terms: 3.515625 + 3.75x + x2 = 2.625 + 3.515625 Combine like terms: 2.625 + 3.515625 = 6.140625 3.515625 + 3.75x + x2 = 6.140625 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = 6.140625 Calculate the square root of the right side: 2.47802845 Break this problem into two subproblems by setting (x + 1.875) equal to 2.47802845 and -2.47802845.

Subproblem 1

x + 1.875 = 2.47802845 Simplifying x + 1.875 = 2.47802845 Reorder the terms: 1.875 + x = 2.47802845 Solving 1.875 + x = 2.47802845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = 2.47802845 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 2.47802845 + -1.875 x = 2.47802845 + -1.875 Combine like terms: 2.47802845 + -1.875 = 0.60302845 x = 0.60302845 Simplifying x = 0.60302845

Subproblem 2

x + 1.875 = -2.47802845 Simplifying x + 1.875 = -2.47802845 Reorder the terms: 1.875 + x = -2.47802845 Solving 1.875 + x = -2.47802845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = -2.47802845 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -2.47802845 + -1.875 x = -2.47802845 + -1.875 Combine like terms: -2.47802845 + -1.875 = -4.35302845 x = -4.35302845 Simplifying x = -4.35302845

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.60302845, -4.35302845}

Solution

x = {0.60302845, -4.35302845}

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