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Simplifying 5x2 + 37x + 20 = 0 Reorder the terms: 20 + 37x + 5x2 = 0 Solving 20 + 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'. 4 + 7.4x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 7.4x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 7.4x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 7.4x + x2 = 0 + -4 7.4x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 7.4x + x2 = -4 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 = -4 + 13.69 Reorder the terms: 13.69 + 7.4x + x2 = -4 + 13.69 Combine like terms: -4 + 13.69 = 9.69 13.69 + 7.4x + x2 = 9.69 Factor a perfect square on the left side: (x + 3.7)(x + 3.7) = 9.69 Calculate the square root of the right side: 3.112876483 Break this problem into two subproblems by setting (x + 3.7) equal to 3.112876483 and -3.112876483.Subproblem 1
x + 3.7 = 3.112876483 Simplifying x + 3.7 = 3.112876483 Reorder the terms: 3.7 + x = 3.112876483 Solving 3.7 + x = 3.112876483 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 = 3.112876483 + -3.7 Combine like terms: 3.7 + -3.7 = 0.0 0.0 + x = 3.112876483 + -3.7 x = 3.112876483 + -3.7 Combine like terms: 3.112876483 + -3.7 = -0.587123517 x = -0.587123517 Simplifying x = -0.587123517Subproblem 2
x + 3.7 = -3.112876483 Simplifying x + 3.7 = -3.112876483 Reorder the terms: 3.7 + x = -3.112876483 Solving 3.7 + x = -3.112876483 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 = -3.112876483 + -3.7 Combine like terms: 3.7 + -3.7 = 0.0 0.0 + x = -3.112876483 + -3.7 x = -3.112876483 + -3.7 Combine like terms: -3.112876483 + -3.7 = -6.812876483 x = -6.812876483 Simplifying x = -6.812876483Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.587123517, -6.812876483}
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