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Simplifying 3x2 + -42x + 68 = 0 Reorder the terms: 68 + -42x + 3x2 = 0 Solving 68 + -42x + 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'. 22.66666667 + -14x + x2 = 0 Move the constant term to the right: Add '-22.66666667' to each side of the equation. 22.66666667 + -14x + -22.66666667 + x2 = 0 + -22.66666667 Reorder the terms: 22.66666667 + -22.66666667 + -14x + x2 = 0 + -22.66666667 Combine like terms: 22.66666667 + -22.66666667 = 0.00000000 0.00000000 + -14x + x2 = 0 + -22.66666667 -14x + x2 = 0 + -22.66666667 Combine like terms: 0 + -22.66666667 = -22.66666667 -14x + x2 = -22.66666667 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -22.66666667 + 49 Reorder the terms: 49 + -14x + x2 = -22.66666667 + 49 Combine like terms: -22.66666667 + 49 = 26.33333333 49 + -14x + x2 = 26.33333333 Factor a perfect square on the left side: (x + -7)(x + -7) = 26.33333333 Calculate the square root of the right side: 5.131601439 Break this problem into two subproblems by setting (x + -7) equal to 5.131601439 and -5.131601439.Subproblem 1
x + -7 = 5.131601439 Simplifying x + -7 = 5.131601439 Reorder the terms: -7 + x = 5.131601439 Solving -7 + x = 5.131601439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 5.131601439 + 7 Combine like terms: -7 + 7 = 0 0 + x = 5.131601439 + 7 x = 5.131601439 + 7 Combine like terms: 5.131601439 + 7 = 12.131601439 x = 12.131601439 Simplifying x = 12.131601439Subproblem 2
x + -7 = -5.131601439 Simplifying x + -7 = -5.131601439 Reorder the terms: -7 + x = -5.131601439 Solving -7 + x = -5.131601439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -5.131601439 + 7 Combine like terms: -7 + 7 = 0 0 + x = -5.131601439 + 7 x = -5.131601439 + 7 Combine like terms: -5.131601439 + 7 = 1.868398561 x = 1.868398561 Simplifying x = 1.868398561Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.131601439, 1.868398561}
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