8b^2-10b-6=0

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Solution for 8b^2-10b-6=0 equation:


Simplifying
8b2 + -10b + -6 = 0

Reorder the terms:
-6 + -10b + 8b2 = 0

Solving
-6 + -10b + 8b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -5b + 4b2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-3 + -5b + 4b2)' equal to zero and attempt to solve: Simplifying -3 + -5b + 4b2 = 0 Solving -3 + -5b + 4b2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + -1.25b + b2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -1.25b + 0.75 + b2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -1.25b + b2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -1.25b + b2 = 0 + 0.75 -1.25b + b2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -1.25b + b2 = 0.75 The b term is -1.25b. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25b + 0.390625 + b2 = 0.75 + 0.390625 Reorder the terms: 0.390625 + -1.25b + b2 = 0.75 + 0.390625 Combine like terms: 0.75 + 0.390625 = 1.140625 0.390625 + -1.25b + b2 = 1.140625 Factor a perfect square on the left side: (b + -0.625)(b + -0.625) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (b + -0.625) equal to 1.068000468 and -1.068000468.

Subproblem 1

b + -0.625 = 1.068000468 Simplifying b + -0.625 = 1.068000468 Reorder the terms: -0.625 + b = 1.068000468 Solving -0.625 + b = 1.068000468 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + b = 1.068000468 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + b = 1.068000468 + 0.625 b = 1.068000468 + 0.625 Combine like terms: 1.068000468 + 0.625 = 1.693000468 b = 1.693000468 Simplifying b = 1.693000468

Subproblem 2

b + -0.625 = -1.068000468 Simplifying b + -0.625 = -1.068000468 Reorder the terms: -0.625 + b = -1.068000468 Solving -0.625 + b = -1.068000468 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + b = -1.068000468 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + b = -1.068000468 + 0.625 b = -1.068000468 + 0.625 Combine like terms: -1.068000468 + 0.625 = -0.443000468 b = -0.443000468 Simplifying b = -0.443000468

Solution

The solution to the problem is based on the solutions from the subproblems. b = {1.693000468, -0.443000468}

Solution

b = {1.693000468, -0.443000468}

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