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Simplifying -10b2 + 30b + 70 = 0 Reorder the terms: 70 + 30b + -10b2 = 0 Solving 70 + 30b + -10b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '10'. 10(7 + 3b + -1b2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(7 + 3b + -1b2)' equal to zero and attempt to solve: Simplifying 7 + 3b + -1b2 = 0 Solving 7 + 3b + -1b2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7 + -3b + b2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -3b + 7 + b2 = 0 + 7 Reorder the terms: -7 + 7 + -3b + b2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3b + b2 = 0 + 7 -3b + b2 = 0 + 7 Combine like terms: 0 + 7 = 7 -3b + b2 = 7 The b term is -3b. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3b + 2.25 + b2 = 7 + 2.25 Reorder the terms: 2.25 + -3b + b2 = 7 + 2.25 Combine like terms: 7 + 2.25 = 9.25 2.25 + -3b + b2 = 9.25 Factor a perfect square on the left side: (b + -1.5)(b + -1.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (b + -1.5) equal to 3.041381265 and -3.041381265.Subproblem 1
b + -1.5 = 3.041381265 Simplifying b + -1.5 = 3.041381265 Reorder the terms: -1.5 + b = 3.041381265 Solving -1.5 + b = 3.041381265 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + b = 3.041381265 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + b = 3.041381265 + 1.5 b = 3.041381265 + 1.5 Combine like terms: 3.041381265 + 1.5 = 4.541381265 b = 4.541381265 Simplifying b = 4.541381265Subproblem 2
b + -1.5 = -3.041381265 Simplifying b + -1.5 = -3.041381265 Reorder the terms: -1.5 + b = -3.041381265 Solving -1.5 + b = -3.041381265 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + b = -3.041381265 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + b = -3.041381265 + 1.5 b = -3.041381265 + 1.5 Combine like terms: -3.041381265 + 1.5 = -1.541381265 b = -1.541381265 Simplifying b = -1.541381265Solution
The solution to the problem is based on the solutions from the subproblems. b = {4.541381265, -1.541381265}Solution
b = {4.541381265, -1.541381265}
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