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Simplifying 5x2 + 37x + -8 = 0 Reorder the terms: -8 + 37x + 5x2 = 0 Solving -8 + 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'. -1.6 + 7.4x + x2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + 7.4x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + 7.4x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + 7.4x + x2 = 0 + 1.6 7.4x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 7.4x + x2 = 1.6 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 = 1.6 + 13.69 Reorder the terms: 13.69 + 7.4x + x2 = 1.6 + 13.69 Combine like terms: 1.6 + 13.69 = 15.29 13.69 + 7.4x + x2 = 15.29 Factor a perfect square on the left side: (x + 3.7)(x + 3.7) = 15.29 Calculate the square root of the right side: 3.910242959 Break this problem into two subproblems by setting (x + 3.7) equal to 3.910242959 and -3.910242959.Subproblem 1
x + 3.7 = 3.910242959 Simplifying x + 3.7 = 3.910242959 Reorder the terms: 3.7 + x = 3.910242959 Solving 3.7 + x = 3.910242959 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 = 3.910242959 + -3.7 Combine like terms: 3.7 + -3.7 = 0.0 0.0 + x = 3.910242959 + -3.7 x = 3.910242959 + -3.7 Combine like terms: 3.910242959 + -3.7 = 0.210242959 x = 0.210242959 Simplifying x = 0.210242959Subproblem 2
x + 3.7 = -3.910242959 Simplifying x + 3.7 = -3.910242959 Reorder the terms: 3.7 + x = -3.910242959 Solving 3.7 + x = -3.910242959 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 = -3.910242959 + -3.7 Combine like terms: 3.7 + -3.7 = 0.0 0.0 + x = -3.910242959 + -3.7 x = -3.910242959 + -3.7 Combine like terms: -3.910242959 + -3.7 = -7.610242959 x = -7.610242959 Simplifying x = -7.610242959Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.210242959, -7.610242959}
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