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Simplifying 16x2 + 18x + 1 = 0 Reorder the terms: 1 + 18x + 16x2 = 0 Solving 1 + 18x + 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 + 1.125x + x2 = 0 Move the constant term to the right: Add '-0.0625' to each side of the equation. 0.0625 + 1.125x + -0.0625 + x2 = 0 + -0.0625 Reorder the terms: 0.0625 + -0.0625 + 1.125x + x2 = 0 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + 1.125x + x2 = 0 + -0.0625 1.125x + x2 = 0 + -0.0625 Combine like terms: 0 + -0.0625 = -0.0625 1.125x + x2 = -0.0625 The x term is 1.125x. Take half its coefficient (0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. 1.125x + 0.31640625 + x2 = -0.0625 + 0.31640625 Reorder the terms: 0.31640625 + 1.125x + x2 = -0.0625 + 0.31640625 Combine like terms: -0.0625 + 0.31640625 = 0.25390625 0.31640625 + 1.125x + x2 = 0.25390625 Factor a perfect square on the left side: (x + 0.5625)(x + 0.5625) = 0.25390625 Calculate the square root of the right side: 0.503891109 Break this problem into two subproblems by setting (x + 0.5625) equal to 0.503891109 and -0.503891109.Subproblem 1
x + 0.5625 = 0.503891109 Simplifying x + 0.5625 = 0.503891109 Reorder the terms: 0.5625 + x = 0.503891109 Solving 0.5625 + x = 0.503891109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = 0.503891109 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = 0.503891109 + -0.5625 x = 0.503891109 + -0.5625 Combine like terms: 0.503891109 + -0.5625 = -0.058608891 x = -0.058608891 Simplifying x = -0.058608891Subproblem 2
x + 0.5625 = -0.503891109 Simplifying x + 0.5625 = -0.503891109 Reorder the terms: 0.5625 + x = -0.503891109 Solving 0.5625 + x = -0.503891109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = -0.503891109 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = -0.503891109 + -0.5625 x = -0.503891109 + -0.5625 Combine like terms: -0.503891109 + -0.5625 = -1.066391109 x = -1.066391109 Simplifying x = -1.066391109Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.058608891, -1.066391109}
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