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Simplifying 3x2 + -21x + 31 = 0 Reorder the terms: 31 + -21x + 3x2 = 0 Solving 31 + -21x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 10.33333333 + -7x + x2 = 0 Move the constant term to the right: Add '-10.33333333' to each side of the equation. 10.33333333 + -7x + -10.33333333 + x2 = 0 + -10.33333333 Reorder the terms: 10.33333333 + -10.33333333 + -7x + x2 = 0 + -10.33333333 Combine like terms: 10.33333333 + -10.33333333 = 0.00000000 0.00000000 + -7x + x2 = 0 + -10.33333333 -7x + x2 = 0 + -10.33333333 Combine like terms: 0 + -10.33333333 = -10.33333333 -7x + x2 = -10.33333333 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -10.33333333 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -10.33333333 + 12.25 Combine like terms: -10.33333333 + 12.25 = 1.91666667 12.25 + -7x + x2 = 1.91666667 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 1.91666667 Calculate the square root of the right side: 1.384437312 Break this problem into two subproblems by setting (x + -3.5) equal to 1.384437312 and -1.384437312.Subproblem 1
x + -3.5 = 1.384437312 Simplifying x + -3.5 = 1.384437312 Reorder the terms: -3.5 + x = 1.384437312 Solving -3.5 + x = 1.384437312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 1.384437312 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 1.384437312 + 3.5 x = 1.384437312 + 3.5 Combine like terms: 1.384437312 + 3.5 = 4.884437312 x = 4.884437312 Simplifying x = 4.884437312Subproblem 2
x + -3.5 = -1.384437312 Simplifying x + -3.5 = -1.384437312 Reorder the terms: -3.5 + x = -1.384437312 Solving -3.5 + x = -1.384437312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -1.384437312 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -1.384437312 + 3.5 x = -1.384437312 + 3.5 Combine like terms: -1.384437312 + 3.5 = 2.115562688 x = 2.115562688 Simplifying x = 2.115562688Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.884437312, 2.115562688}
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