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Simplifying 7x2 + -42x + 43 = 0 Reorder the terms: 43 + -42x + 7x2 = 0 Solving 43 + -42x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 6.142857143 + -6x + x2 = 0 Move the constant term to the right: Add '-6.142857143' to each side of the equation. 6.142857143 + -6x + -6.142857143 + x2 = 0 + -6.142857143 Reorder the terms: 6.142857143 + -6.142857143 + -6x + x2 = 0 + -6.142857143 Combine like terms: 6.142857143 + -6.142857143 = 0.000000000 0.000000000 + -6x + x2 = 0 + -6.142857143 -6x + x2 = 0 + -6.142857143 Combine like terms: 0 + -6.142857143 = -6.142857143 -6x + x2 = -6.142857143 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -6.142857143 + 9 Reorder the terms: 9 + -6x + x2 = -6.142857143 + 9 Combine like terms: -6.142857143 + 9 = 2.857142857 9 + -6x + x2 = 2.857142857 Factor a perfect square on the left side: (x + -3)(x + -3) = 2.857142857 Calculate the square root of the right side: 1.690308509 Break this problem into two subproblems by setting (x + -3) equal to 1.690308509 and -1.690308509.Subproblem 1
x + -3 = 1.690308509 Simplifying x + -3 = 1.690308509 Reorder the terms: -3 + x = 1.690308509 Solving -3 + x = 1.690308509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 1.690308509 + 3 Combine like terms: -3 + 3 = 0 0 + x = 1.690308509 + 3 x = 1.690308509 + 3 Combine like terms: 1.690308509 + 3 = 4.690308509 x = 4.690308509 Simplifying x = 4.690308509Subproblem 2
x + -3 = -1.690308509 Simplifying x + -3 = -1.690308509 Reorder the terms: -3 + x = -1.690308509 Solving -3 + x = -1.690308509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -1.690308509 + 3 Combine like terms: -3 + 3 = 0 0 + x = -1.690308509 + 3 x = -1.690308509 + 3 Combine like terms: -1.690308509 + 3 = 1.309691491 x = 1.309691491 Simplifying x = 1.309691491Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.690308509, 1.309691491}
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