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Simplifying 5x2 + 37x + -51 = 0 Reorder the terms: -51 + 37x + 5x2 = 0 Solving -51 + 37x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -10.2 + 7.4x + x2 = 0 Move the constant term to the right: Add '10.2' to each side of the equation. -10.2 + 7.4x + 10.2 + x2 = 0 + 10.2 Reorder the terms: -10.2 + 10.2 + 7.4x + x2 = 0 + 10.2 Combine like terms: -10.2 + 10.2 = 0.0 0.0 + 7.4x + x2 = 0 + 10.2 7.4x + x2 = 0 + 10.2 Combine like terms: 0 + 10.2 = 10.2 7.4x + x2 = 10.2 The x term is 7.4x. Take half its coefficient (3.7). Square it (13.69) and add it to both sides. Add '13.69' to each side of the equation. 7.4x + 13.69 + x2 = 10.2 + 13.69 Reorder the terms: 13.69 + 7.4x + x2 = 10.2 + 13.69 Combine like terms: 10.2 + 13.69 = 23.89 13.69 + 7.4x + x2 = 23.89 Factor a perfect square on the left side: (x + 3.7)(x + 3.7) = 23.89 Calculate the square root of the right side: 4.887739764 Break this problem into two subproblems by setting (x + 3.7) equal to 4.887739764 and -4.887739764.Subproblem 1
x + 3.7 = 4.887739764 Simplifying x + 3.7 = 4.887739764 Reorder the terms: 3.7 + x = 4.887739764 Solving 3.7 + x = 4.887739764 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.7' to each side of the equation. 3.7 + -3.7 + x = 4.887739764 + -3.7 Combine like terms: 3.7 + -3.7 = 0.0 0.0 + x = 4.887739764 + -3.7 x = 4.887739764 + -3.7 Combine like terms: 4.887739764 + -3.7 = 1.187739764 x = 1.187739764 Simplifying x = 1.187739764Subproblem 2
x + 3.7 = -4.887739764 Simplifying x + 3.7 = -4.887739764 Reorder the terms: 3.7 + x = -4.887739764 Solving 3.7 + x = -4.887739764 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.7' to each side of the equation. 3.7 + -3.7 + x = -4.887739764 + -3.7 Combine like terms: 3.7 + -3.7 = 0.0 0.0 + x = -4.887739764 + -3.7 x = -4.887739764 + -3.7 Combine like terms: -4.887739764 + -3.7 = -8.587739764 x = -8.587739764 Simplifying x = -8.587739764Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.187739764, -8.587739764}
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