-2b^2+10b+40=0

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Solution for -2b^2+10b+40=0 equation:


Simplifying
-2b2 + 10b + 40 = 0

Reorder the terms:
40 + 10b + -2b2 = 0

Solving
40 + 10b + -2b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '2'.
2(20 + 5b + -1b2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(20 + 5b + -1b2)' equal to zero and attempt to solve: Simplifying 20 + 5b + -1b2 = 0 Solving 20 + 5b + -1b2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -20 + -5b + b2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -5b + 20 + b2 = 0 + 20 Reorder the terms: -20 + 20 + -5b + b2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -5b + b2 = 0 + 20 -5b + b2 = 0 + 20 Combine like terms: 0 + 20 = 20 -5b + b2 = 20 The b term is -5b. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5b + 6.25 + b2 = 20 + 6.25 Reorder the terms: 6.25 + -5b + b2 = 20 + 6.25 Combine like terms: 20 + 6.25 = 26.25 6.25 + -5b + b2 = 26.25 Factor a perfect square on the left side: (b + -2.5)(b + -2.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (b + -2.5) equal to 5.123475383 and -5.123475383.

Subproblem 1

b + -2.5 = 5.123475383 Simplifying b + -2.5 = 5.123475383 Reorder the terms: -2.5 + b = 5.123475383 Solving -2.5 + b = 5.123475383 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + b = 5.123475383 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + b = 5.123475383 + 2.5 b = 5.123475383 + 2.5 Combine like terms: 5.123475383 + 2.5 = 7.623475383 b = 7.623475383 Simplifying b = 7.623475383

Subproblem 2

b + -2.5 = -5.123475383 Simplifying b + -2.5 = -5.123475383 Reorder the terms: -2.5 + b = -5.123475383 Solving -2.5 + b = -5.123475383 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + b = -5.123475383 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + b = -5.123475383 + 2.5 b = -5.123475383 + 2.5 Combine like terms: -5.123475383 + 2.5 = -2.623475383 b = -2.623475383 Simplifying b = -2.623475383

Solution

The solution to the problem is based on the solutions from the subproblems. b = {7.623475383, -2.623475383}

Solution

b = {7.623475383, -2.623475383}

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