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Simplifying 16x2 + 5x + -24 = 124 Reorder the terms: -24 + 5x + 16x2 = 124 Solving -24 + 5x + 16x2 = 124 Solving for variable 'x'. Reorder the terms: -24 + -124 + 5x + 16x2 = 124 + -124 Combine like terms: -24 + -124 = -148 -148 + 5x + 16x2 = 124 + -124 Combine like terms: 124 + -124 = 0 -148 + 5x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -9.25 + 0.3125x + x2 = 0 Move the constant term to the right: Add '9.25' to each side of the equation. -9.25 + 0.3125x + 9.25 + x2 = 0 + 9.25 Reorder the terms: -9.25 + 9.25 + 0.3125x + x2 = 0 + 9.25 Combine like terms: -9.25 + 9.25 = 0.00 0.00 + 0.3125x + x2 = 0 + 9.25 0.3125x + x2 = 0 + 9.25 Combine like terms: 0 + 9.25 = 9.25 0.3125x + x2 = 9.25 The x term is 0.3125x. Take half its coefficient (0.15625). Square it (0.0244140625) and add it to both sides. Add '0.0244140625' to each side of the equation. 0.3125x + 0.0244140625 + x2 = 9.25 + 0.0244140625 Reorder the terms: 0.0244140625 + 0.3125x + x2 = 9.25 + 0.0244140625 Combine like terms: 9.25 + 0.0244140625 = 9.2744140625 0.0244140625 + 0.3125x + x2 = 9.2744140625 Factor a perfect square on the left side: (x + 0.15625)(x + 0.15625) = 9.2744140625 Calculate the square root of the right side: 3.045392267 Break this problem into two subproblems by setting (x + 0.15625) equal to 3.045392267 and -3.045392267.Subproblem 1
x + 0.15625 = 3.045392267 Simplifying x + 0.15625 = 3.045392267 Reorder the terms: 0.15625 + x = 3.045392267 Solving 0.15625 + x = 3.045392267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15625' to each side of the equation. 0.15625 + -0.15625 + x = 3.045392267 + -0.15625 Combine like terms: 0.15625 + -0.15625 = 0.00000 0.00000 + x = 3.045392267 + -0.15625 x = 3.045392267 + -0.15625 Combine like terms: 3.045392267 + -0.15625 = 2.889142267 x = 2.889142267 Simplifying x = 2.889142267Subproblem 2
x + 0.15625 = -3.045392267 Simplifying x + 0.15625 = -3.045392267 Reorder the terms: 0.15625 + x = -3.045392267 Solving 0.15625 + x = -3.045392267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15625' to each side of the equation. 0.15625 + -0.15625 + x = -3.045392267 + -0.15625 Combine like terms: 0.15625 + -0.15625 = 0.00000 0.00000 + x = -3.045392267 + -0.15625 x = -3.045392267 + -0.15625 Combine like terms: -3.045392267 + -0.15625 = -3.201642267 x = -3.201642267 Simplifying x = -3.201642267Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.889142267, -3.201642267}
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