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Simplifying 252 = (6x + -7)(x) Reorder the terms: 252 = (-7 + 6x)(x) Reorder the terms for easier multiplication: 252 = x(-7 + 6x) 252 = (-7 * x + 6x * x) 252 = (-7x + 6x2) Solving 252 = -7x + 6x2 Solving for variable 'x'. Reorder the terms: 252 + 7x + -6x2 = -7x + 7x + 6x2 + -6x2 Combine like terms: -7x + 7x = 0 252 + 7x + -6x2 = 0 + 6x2 + -6x2 252 + 7x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 252 + 7x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -42 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '42' to each side of the equation. -42 + -1.166666667x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + -1.166666667x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -1.166666667x + x2 = 0 + 42 -1.166666667x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 -1.166666667x + x2 = 42 The x term is -1.166666667x. Take half its coefficient (-0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. -1.166666667x + 0.3402777780 + x2 = 42 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 42 + 0.3402777780 Combine like terms: 42 + 0.3402777780 = 42.340277778 0.3402777780 + -1.166666667x + x2 = 42.340277778 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 42.340277778 Calculate the square root of the right side: 6.506940739 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 6.506940739 and -6.506940739.Subproblem 1
x + -0.5833333335 = 6.506940739 Simplifying x + -0.5833333335 = 6.506940739 Reorder the terms: -0.5833333335 + x = 6.506940739 Solving -0.5833333335 + x = 6.506940739 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = 6.506940739 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 6.506940739 + 0.5833333335 x = 6.506940739 + 0.5833333335 Combine like terms: 6.506940739 + 0.5833333335 = 7.0902740725 x = 7.0902740725 Simplifying x = 7.0902740725Subproblem 2
x + -0.5833333335 = -6.506940739 Simplifying x + -0.5833333335 = -6.506940739 Reorder the terms: -0.5833333335 + x = -6.506940739 Solving -0.5833333335 + x = -6.506940739 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = -6.506940739 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -6.506940739 + 0.5833333335 x = -6.506940739 + 0.5833333335 Combine like terms: -6.506940739 + 0.5833333335 = -5.9236074055 x = -5.9236074055 Simplifying x = -5.9236074055Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.0902740725, -5.9236074055}
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