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Simplifying 35x2 + x + 6 = 0 Reorder the terms: 6 + x + 35x2 = 0 Solving 6 + x + 35x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. 0.1714285714 + 0.02857142857x + x2 = 0 Move the constant term to the right: Add '-0.1714285714' to each side of the equation. 0.1714285714 + 0.02857142857x + -0.1714285714 + x2 = 0 + -0.1714285714 Reorder the terms: 0.1714285714 + -0.1714285714 + 0.02857142857x + x2 = 0 + -0.1714285714 Combine like terms: 0.1714285714 + -0.1714285714 = 0.0000000000 0.0000000000 + 0.02857142857x + x2 = 0 + -0.1714285714 0.02857142857x + x2 = 0 + -0.1714285714 Combine like terms: 0 + -0.1714285714 = -0.1714285714 0.02857142857x + x2 = -0.1714285714 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.02857142857x + 0.25 + x2 = -0.1714285714 + 0.25 Reorder the terms: 0.25 + 0.02857142857x + x2 = -0.1714285714 + 0.25 Combine like terms: -0.1714285714 + 0.25 = 0.0785714286 0.25 + 0.02857142857x + x2 = 0.0785714286 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.0785714286 Calculate the square root of the right side: 0.280305955 Break this problem into two subproblems by setting (x + 0.5) equal to 0.280305955 and -0.280305955.Subproblem 1
x + 0.5 = 0.280305955 Simplifying x + 0.5 = 0.280305955 Reorder the terms: 0.5 + x = 0.280305955 Solving 0.5 + x = 0.280305955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.280305955 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.280305955 + -0.5 x = 0.280305955 + -0.5 Combine like terms: 0.280305955 + -0.5 = -0.219694045 x = -0.219694045 Simplifying x = -0.219694045Subproblem 2
x + 0.5 = -0.280305955 Simplifying x + 0.5 = -0.280305955 Reorder the terms: 0.5 + x = -0.280305955 Solving 0.5 + x = -0.280305955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.280305955 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.280305955 + -0.5 x = -0.280305955 + -0.5 Combine like terms: -0.280305955 + -0.5 = -0.780305955 x = -0.780305955 Simplifying x = -0.780305955Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.219694045, -0.780305955}
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