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Simplifying 16x2 + 26x + -64 = 0 Reorder the terms: -64 + 26x + 16x2 = 0 Solving -64 + 26x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-32 + 13x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-32 + 13x + 8x2)' equal to zero and attempt to solve: Simplifying -32 + 13x + 8x2 = 0 Solving -32 + 13x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -4 + 1.625x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 1.625x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 1.625x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 1.625x + x2 = 0 + 4 1.625x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 1.625x + x2 = 4 The x term is 1.625x. Take half its coefficient (0.8125). Square it (0.66015625) and add it to both sides. Add '0.66015625' to each side of the equation. 1.625x + 0.66015625 + x2 = 4 + 0.66015625 Reorder the terms: 0.66015625 + 1.625x + x2 = 4 + 0.66015625 Combine like terms: 4 + 0.66015625 = 4.66015625 0.66015625 + 1.625x + x2 = 4.66015625 Factor a perfect square on the left side: (x + 0.8125)(x + 0.8125) = 4.66015625 Calculate the square root of the right side: 2.158739505 Break this problem into two subproblems by setting (x + 0.8125) equal to 2.158739505 and -2.158739505.Subproblem 1
x + 0.8125 = 2.158739505 Simplifying x + 0.8125 = 2.158739505 Reorder the terms: 0.8125 + x = 2.158739505 Solving 0.8125 + x = 2.158739505 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8125' to each side of the equation. 0.8125 + -0.8125 + x = 2.158739505 + -0.8125 Combine like terms: 0.8125 + -0.8125 = 0.0000 0.0000 + x = 2.158739505 + -0.8125 x = 2.158739505 + -0.8125 Combine like terms: 2.158739505 + -0.8125 = 1.346239505 x = 1.346239505 Simplifying x = 1.346239505Subproblem 2
x + 0.8125 = -2.158739505 Simplifying x + 0.8125 = -2.158739505 Reorder the terms: 0.8125 + x = -2.158739505 Solving 0.8125 + x = -2.158739505 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8125' to each side of the equation. 0.8125 + -0.8125 + x = -2.158739505 + -0.8125 Combine like terms: 0.8125 + -0.8125 = 0.0000 0.0000 + x = -2.158739505 + -0.8125 x = -2.158739505 + -0.8125 Combine like terms: -2.158739505 + -0.8125 = -2.971239505 x = -2.971239505 Simplifying x = -2.971239505Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.346239505, -2.971239505}Solution
x = {1.346239505, -2.971239505}
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