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Simplifying 7x2 + 4x + -720 = 0 Reorder the terms: -720 + 4x + 7x2 = 0 Solving -720 + 4x + 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 + 0.5714285714x + x2 = 0 Move the constant term to the right: Add '102.8571429' to each side of the equation. -102.8571429 + 0.5714285714x + 102.8571429 + x2 = 0 + 102.8571429 Reorder the terms: -102.8571429 + 102.8571429 + 0.5714285714x + x2 = 0 + 102.8571429 Combine like terms: -102.8571429 + 102.8571429 = 0.0000000 0.0000000 + 0.5714285714x + x2 = 0 + 102.8571429 0.5714285714x + x2 = 0 + 102.8571429 Combine like terms: 0 + 102.8571429 = 102.8571429 0.5714285714x + x2 = 102.8571429 The x term is 0.5714285714x. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714x + 0.08163265305 + x2 = 102.8571429 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714x + x2 = 102.8571429 + 0.08163265305 Combine like terms: 102.8571429 + 0.08163265305 = 102.93877555305 0.08163265305 + 0.5714285714x + x2 = 102.93877555305 Factor a perfect square on the left side: (x + 0.2857142857)(x + 0.2857142857) = 102.93877555305 Calculate the square root of the right side: 10.145874805 Break this problem into two subproblems by setting (x + 0.2857142857) equal to 10.145874805 and -10.145874805.Subproblem 1
x + 0.2857142857 = 10.145874805 Simplifying x + 0.2857142857 = 10.145874805 Reorder the terms: 0.2857142857 + x = 10.145874805 Solving 0.2857142857 + x = 10.145874805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = 10.145874805 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = 10.145874805 + -0.2857142857 x = 10.145874805 + -0.2857142857 Combine like terms: 10.145874805 + -0.2857142857 = 9.8601605193 x = 9.8601605193 Simplifying x = 9.8601605193Subproblem 2
x + 0.2857142857 = -10.145874805 Simplifying x + 0.2857142857 = -10.145874805 Reorder the terms: 0.2857142857 + x = -10.145874805 Solving 0.2857142857 + x = -10.145874805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = -10.145874805 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = -10.145874805 + -0.2857142857 x = -10.145874805 + -0.2857142857 Combine like terms: -10.145874805 + -0.2857142857 = -10.4315890907 x = -10.4315890907 Simplifying x = -10.4315890907Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.8601605193, -10.4315890907}
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