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Simplifying 7x2 + 84x + -720 = 0 Reorder the terms: -720 + 84x + 7x2 = 0 Solving -720 + 84x + 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'. -102.8571429 + 12x + x2 = 0 Move the constant term to the right: Add '102.8571429' to each side of the equation. -102.8571429 + 12x + 102.8571429 + x2 = 0 + 102.8571429 Reorder the terms: -102.8571429 + 102.8571429 + 12x + x2 = 0 + 102.8571429 Combine like terms: -102.8571429 + 102.8571429 = 0.0000000 0.0000000 + 12x + x2 = 0 + 102.8571429 12x + x2 = 0 + 102.8571429 Combine like terms: 0 + 102.8571429 = 102.8571429 12x + x2 = 102.8571429 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 102.8571429 + 36 Reorder the terms: 36 + 12x + x2 = 102.8571429 + 36 Combine like terms: 102.8571429 + 36 = 138.8571429 36 + 12x + x2 = 138.8571429 Factor a perfect square on the left side: (x + 6)(x + 6) = 138.8571429 Calculate the square root of the right side: 11.783766075 Break this problem into two subproblems by setting (x + 6) equal to 11.783766075 and -11.783766075.Subproblem 1
x + 6 = 11.783766075 Simplifying x + 6 = 11.783766075 Reorder the terms: 6 + x = 11.783766075 Solving 6 + x = 11.783766075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 11.783766075 + -6 Combine like terms: 6 + -6 = 0 0 + x = 11.783766075 + -6 x = 11.783766075 + -6 Combine like terms: 11.783766075 + -6 = 5.783766075 x = 5.783766075 Simplifying x = 5.783766075Subproblem 2
x + 6 = -11.783766075 Simplifying x + 6 = -11.783766075 Reorder the terms: 6 + x = -11.783766075 Solving 6 + x = -11.783766075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -11.783766075 + -6 Combine like terms: 6 + -6 = 0 0 + x = -11.783766075 + -6 x = -11.783766075 + -6 Combine like terms: -11.783766075 + -6 = -17.783766075 x = -17.783766075 Simplifying x = -17.783766075Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.783766075, -17.783766075}
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