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Simplifying 16x2 + 50x + 14 = 0 Reorder the terms: 14 + 50x + 16x2 = 0 Solving 14 + 50x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + 25x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + 25x + 8x2)' equal to zero and attempt to solve: Simplifying 7 + 25x + 8x2 = 0 Solving 7 + 25x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.875 + 3.125x + x2 = 0 Move the constant term to the right: Add '-0.875' to each side of the equation. 0.875 + 3.125x + -0.875 + x2 = 0 + -0.875 Reorder the terms: 0.875 + -0.875 + 3.125x + x2 = 0 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + 3.125x + x2 = 0 + -0.875 3.125x + x2 = 0 + -0.875 Combine like terms: 0 + -0.875 = -0.875 3.125x + x2 = -0.875 The x term is 3.125x. Take half its coefficient (1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. 3.125x + 2.44140625 + x2 = -0.875 + 2.44140625 Reorder the terms: 2.44140625 + 3.125x + x2 = -0.875 + 2.44140625 Combine like terms: -0.875 + 2.44140625 = 1.56640625 2.44140625 + 3.125x + x2 = 1.56640625 Factor a perfect square on the left side: (x + 1.5625)(x + 1.5625) = 1.56640625 Calculate the square root of the right side: 1.251561525 Break this problem into two subproblems by setting (x + 1.5625) equal to 1.251561525 and -1.251561525.Subproblem 1
x + 1.5625 = 1.251561525 Simplifying x + 1.5625 = 1.251561525 Reorder the terms: 1.5625 + x = 1.251561525 Solving 1.5625 + x = 1.251561525 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5625' to each side of the equation. 1.5625 + -1.5625 + x = 1.251561525 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + x = 1.251561525 + -1.5625 x = 1.251561525 + -1.5625 Combine like terms: 1.251561525 + -1.5625 = -0.310938475 x = -0.310938475 Simplifying x = -0.310938475Subproblem 2
x + 1.5625 = -1.251561525 Simplifying x + 1.5625 = -1.251561525 Reorder the terms: 1.5625 + x = -1.251561525 Solving 1.5625 + x = -1.251561525 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5625' to each side of the equation. 1.5625 + -1.5625 + x = -1.251561525 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + x = -1.251561525 + -1.5625 x = -1.251561525 + -1.5625 Combine like terms: -1.251561525 + -1.5625 = -2.814061525 x = -2.814061525 Simplifying x = -2.814061525Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.310938475, -2.814061525}Solution
x = {-0.310938475, -2.814061525}
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