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Simplifying 3x2 + -24x + 34 = 0 Reorder the terms: 34 + -24x + 3x2 = 0 Solving 34 + -24x + 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'. 11.33333333 + -8x + x2 = 0 Move the constant term to the right: Add '-11.33333333' to each side of the equation. 11.33333333 + -8x + -11.33333333 + x2 = 0 + -11.33333333 Reorder the terms: 11.33333333 + -11.33333333 + -8x + x2 = 0 + -11.33333333 Combine like terms: 11.33333333 + -11.33333333 = 0.00000000 0.00000000 + -8x + x2 = 0 + -11.33333333 -8x + x2 = 0 + -11.33333333 Combine like terms: 0 + -11.33333333 = -11.33333333 -8x + x2 = -11.33333333 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -11.33333333 + 16 Reorder the terms: 16 + -8x + x2 = -11.33333333 + 16 Combine like terms: -11.33333333 + 16 = 4.66666667 16 + -8x + x2 = 4.66666667 Factor a perfect square on the left side: (x + -4)(x + -4) = 4.66666667 Calculate the square root of the right side: 2.1602469 Break this problem into two subproblems by setting (x + -4) equal to 2.1602469 and -2.1602469.Subproblem 1
x + -4 = 2.1602469 Simplifying x + -4 = 2.1602469 Reorder the terms: -4 + x = 2.1602469 Solving -4 + x = 2.1602469 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 2.1602469 + 4 Combine like terms: -4 + 4 = 0 0 + x = 2.1602469 + 4 x = 2.1602469 + 4 Combine like terms: 2.1602469 + 4 = 6.1602469 x = 6.1602469 Simplifying x = 6.1602469Subproblem 2
x + -4 = -2.1602469 Simplifying x + -4 = -2.1602469 Reorder the terms: -4 + x = -2.1602469 Solving -4 + x = -2.1602469 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -2.1602469 + 4 Combine like terms: -4 + 4 = 0 0 + x = -2.1602469 + 4 x = -2.1602469 + 4 Combine like terms: -2.1602469 + 4 = 1.8397531 x = 1.8397531 Simplifying x = 1.8397531Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.1602469, 1.8397531}
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