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Simplifying 16x2 + 38x + 4 = 0 Reorder the terms: 4 + 38x + 16x2 = 0 Solving 4 + 38x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 19x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + 19x + 8x2)' equal to zero and attempt to solve: Simplifying 2 + 19x + 8x2 = 0 Solving 2 + 19x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.25 + 2.375x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 2.375x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 2.375x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 2.375x + x2 = 0 + -0.25 2.375x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 2.375x + x2 = -0.25 The x term is 2.375x. Take half its coefficient (1.1875). Square it (1.41015625) and add it to both sides. Add '1.41015625' to each side of the equation. 2.375x + 1.41015625 + x2 = -0.25 + 1.41015625 Reorder the terms: 1.41015625 + 2.375x + x2 = -0.25 + 1.41015625 Combine like terms: -0.25 + 1.41015625 = 1.16015625 1.41015625 + 2.375x + x2 = 1.16015625 Factor a perfect square on the left side: (x + 1.1875)(x + 1.1875) = 1.16015625 Calculate the square root of the right side: 1.077105496 Break this problem into two subproblems by setting (x + 1.1875) equal to 1.077105496 and -1.077105496.Subproblem 1
x + 1.1875 = 1.077105496 Simplifying x + 1.1875 = 1.077105496 Reorder the terms: 1.1875 + x = 1.077105496 Solving 1.1875 + x = 1.077105496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1875' to each side of the equation. 1.1875 + -1.1875 + x = 1.077105496 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + x = 1.077105496 + -1.1875 x = 1.077105496 + -1.1875 Combine like terms: 1.077105496 + -1.1875 = -0.110394504 x = -0.110394504 Simplifying x = -0.110394504Subproblem 2
x + 1.1875 = -1.077105496 Simplifying x + 1.1875 = -1.077105496 Reorder the terms: 1.1875 + x = -1.077105496 Solving 1.1875 + x = -1.077105496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1875' to each side of the equation. 1.1875 + -1.1875 + x = -1.077105496 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + x = -1.077105496 + -1.1875 x = -1.077105496 + -1.1875 Combine like terms: -1.077105496 + -1.1875 = -2.264605496 x = -2.264605496 Simplifying x = -2.264605496Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.110394504, -2.264605496}Solution
x = {-0.110394504, -2.264605496}
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