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Simplifying 16x2 + 25x + 1 = 0 Reorder the terms: 1 + 25x + 16x2 = 0 Solving 1 + 25x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.0625 + 1.5625x + x2 = 0 Move the constant term to the right: Add '-0.0625' to each side of the equation. 0.0625 + 1.5625x + -0.0625 + x2 = 0 + -0.0625 Reorder the terms: 0.0625 + -0.0625 + 1.5625x + x2 = 0 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + 1.5625x + x2 = 0 + -0.0625 1.5625x + x2 = 0 + -0.0625 Combine like terms: 0 + -0.0625 = -0.0625 1.5625x + x2 = -0.0625 The x term is 1.5625x. Take half its coefficient (0.78125). Square it (0.6103515625) and add it to both sides. Add '0.6103515625' to each side of the equation. 1.5625x + 0.6103515625 + x2 = -0.0625 + 0.6103515625 Reorder the terms: 0.6103515625 + 1.5625x + x2 = -0.0625 + 0.6103515625 Combine like terms: -0.0625 + 0.6103515625 = 0.5478515625 0.6103515625 + 1.5625x + x2 = 0.5478515625 Factor a perfect square on the left side: (x + 0.78125)(x + 0.78125) = 0.5478515625 Calculate the square root of the right side: 0.740169955 Break this problem into two subproblems by setting (x + 0.78125) equal to 0.740169955 and -0.740169955.Subproblem 1
x + 0.78125 = 0.740169955 Simplifying x + 0.78125 = 0.740169955 Reorder the terms: 0.78125 + x = 0.740169955 Solving 0.78125 + x = 0.740169955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.78125' to each side of the equation. 0.78125 + -0.78125 + x = 0.740169955 + -0.78125 Combine like terms: 0.78125 + -0.78125 = 0.00000 0.00000 + x = 0.740169955 + -0.78125 x = 0.740169955 + -0.78125 Combine like terms: 0.740169955 + -0.78125 = -0.041080045 x = -0.041080045 Simplifying x = -0.041080045Subproblem 2
x + 0.78125 = -0.740169955 Simplifying x + 0.78125 = -0.740169955 Reorder the terms: 0.78125 + x = -0.740169955 Solving 0.78125 + x = -0.740169955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.78125' to each side of the equation. 0.78125 + -0.78125 + x = -0.740169955 + -0.78125 Combine like terms: 0.78125 + -0.78125 = 0.00000 0.00000 + x = -0.740169955 + -0.78125 x = -0.740169955 + -0.78125 Combine like terms: -0.740169955 + -0.78125 = -1.521419955 x = -1.521419955 Simplifying x = -1.521419955Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.041080045, -1.521419955}
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