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Simplifying 49x2 + 67x + 16 = 0 Reorder the terms: 16 + 67x + 49x2 = 0 Solving 16 + 67x + 49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. 0.3265306122 + 1.367346939x + x2 = 0 Move the constant term to the right: Add '-0.3265306122' to each side of the equation. 0.3265306122 + 1.367346939x + -0.3265306122 + x2 = 0 + -0.3265306122 Reorder the terms: 0.3265306122 + -0.3265306122 + 1.367346939x + x2 = 0 + -0.3265306122 Combine like terms: 0.3265306122 + -0.3265306122 = 0.0000000000 0.0000000000 + 1.367346939x + x2 = 0 + -0.3265306122 1.367346939x + x2 = 0 + -0.3265306122 Combine like terms: 0 + -0.3265306122 = -0.3265306122 1.367346939x + x2 = -0.3265306122 The x term is 1.367346939x. Take half its coefficient (0.6836734695). Square it (0.4674094129) and add it to both sides. Add '0.4674094129' to each side of the equation. 1.367346939x + 0.4674094129 + x2 = -0.3265306122 + 0.4674094129 Reorder the terms: 0.4674094129 + 1.367346939x + x2 = -0.3265306122 + 0.4674094129 Combine like terms: -0.3265306122 + 0.4674094129 = 0.1408788007 0.4674094129 + 1.367346939x + x2 = 0.1408788007 Factor a perfect square on the left side: (x + 0.6836734695)(x + 0.6836734695) = 0.1408788007 Calculate the square root of the right side: 0.375338248 Break this problem into two subproblems by setting (x + 0.6836734695) equal to 0.375338248 and -0.375338248.Subproblem 1
x + 0.6836734695 = 0.375338248 Simplifying x + 0.6836734695 = 0.375338248 Reorder the terms: 0.6836734695 + x = 0.375338248 Solving 0.6836734695 + x = 0.375338248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6836734695' to each side of the equation. 0.6836734695 + -0.6836734695 + x = 0.375338248 + -0.6836734695 Combine like terms: 0.6836734695 + -0.6836734695 = 0.0000000000 0.0000000000 + x = 0.375338248 + -0.6836734695 x = 0.375338248 + -0.6836734695 Combine like terms: 0.375338248 + -0.6836734695 = -0.3083352215 x = -0.3083352215 Simplifying x = -0.3083352215Subproblem 2
x + 0.6836734695 = -0.375338248 Simplifying x + 0.6836734695 = -0.375338248 Reorder the terms: 0.6836734695 + x = -0.375338248 Solving 0.6836734695 + x = -0.375338248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6836734695' to each side of the equation. 0.6836734695 + -0.6836734695 + x = -0.375338248 + -0.6836734695 Combine like terms: 0.6836734695 + -0.6836734695 = 0.0000000000 0.0000000000 + x = -0.375338248 + -0.6836734695 x = -0.375338248 + -0.6836734695 Combine like terms: -0.375338248 + -0.6836734695 = -1.0590117175 x = -1.0590117175 Simplifying x = -1.0590117175Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.3083352215, -1.0590117175}
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