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Simplifying -3x2 + -84x = -123 Reorder the terms: -84x + -3x2 = -123 Solving -84x + -3x2 = -123 Solving for variable 'x'. Reorder the terms: 123 + -84x + -3x2 = -123 + 123 Combine like terms: -123 + 123 = 0 123 + -84x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(41 + -28x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(41 + -28x + -1x2)' equal to zero and attempt to solve: Simplifying 41 + -28x + -1x2 = 0 Solving 41 + -28x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -41 + 28x + x2 = 0 Move the constant term to the right: Add '41' to each side of the equation. -41 + 28x + 41 + x2 = 0 + 41 Reorder the terms: -41 + 41 + 28x + x2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + 28x + x2 = 0 + 41 28x + x2 = 0 + 41 Combine like terms: 0 + 41 = 41 28x + x2 = 41 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = 41 + 196 Reorder the terms: 196 + 28x + x2 = 41 + 196 Combine like terms: 41 + 196 = 237 196 + 28x + x2 = 237 Factor a perfect square on the left side: (x + 14)(x + 14) = 237 Calculate the square root of the right side: 15.394804318 Break this problem into two subproblems by setting (x + 14) equal to 15.394804318 and -15.394804318.Subproblem 1
x + 14 = 15.394804318 Simplifying x + 14 = 15.394804318 Reorder the terms: 14 + x = 15.394804318 Solving 14 + x = 15.394804318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 15.394804318 + -14 Combine like terms: 14 + -14 = 0 0 + x = 15.394804318 + -14 x = 15.394804318 + -14 Combine like terms: 15.394804318 + -14 = 1.394804318 x = 1.394804318 Simplifying x = 1.394804318Subproblem 2
x + 14 = -15.394804318 Simplifying x + 14 = -15.394804318 Reorder the terms: 14 + x = -15.394804318 Solving 14 + x = -15.394804318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -15.394804318 + -14 Combine like terms: 14 + -14 = 0 0 + x = -15.394804318 + -14 x = -15.394804318 + -14 Combine like terms: -15.394804318 + -14 = -29.394804318 x = -29.394804318 Simplifying x = -29.394804318Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.394804318, -29.394804318}Solution
x = {1.394804318, -29.394804318}
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