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Simplifying 6x2 + -21x + 5 = 0 Reorder the terms: 5 + -21x + 6x2 = 0 Solving 5 + -21x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.8333333333 + -3.5x + x2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + -3.5x + -0.8333333333 + x2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + -3.5x + x2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + -3.5x + x2 = 0 + -0.8333333333 -3.5x + x2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 -3.5x + x2 = -0.8333333333 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = -0.8333333333 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -0.8333333333 + 3.0625 Combine like terms: -0.8333333333 + 3.0625 = 2.2291666667 3.0625 + -3.5x + x2 = 2.2291666667 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 2.2291666667 Calculate the square root of the right side: 1.493039406 Break this problem into two subproblems by setting (x + -1.75) equal to 1.493039406 and -1.493039406.Subproblem 1
x + -1.75 = 1.493039406 Simplifying x + -1.75 = 1.493039406 Reorder the terms: -1.75 + x = 1.493039406 Solving -1.75 + x = 1.493039406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 1.493039406 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 1.493039406 + 1.75 x = 1.493039406 + 1.75 Combine like terms: 1.493039406 + 1.75 = 3.243039406 x = 3.243039406 Simplifying x = 3.243039406Subproblem 2
x + -1.75 = -1.493039406 Simplifying x + -1.75 = -1.493039406 Reorder the terms: -1.75 + x = -1.493039406 Solving -1.75 + x = -1.493039406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -1.493039406 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -1.493039406 + 1.75 x = -1.493039406 + 1.75 Combine like terms: -1.493039406 + 1.75 = 0.256960594 x = 0.256960594 Simplifying x = 0.256960594Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.243039406, 0.256960594}
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