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Simplifying 5x2 + 78x + 38 = 0 Reorder the terms: 38 + 78x + 5x2 = 0 Solving 38 + 78x + 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'. 7.6 + 15.6x + x2 = 0 Move the constant term to the right: Add '-7.6' to each side of the equation. 7.6 + 15.6x + -7.6 + x2 = 0 + -7.6 Reorder the terms: 7.6 + -7.6 + 15.6x + x2 = 0 + -7.6 Combine like terms: 7.6 + -7.6 = 0.0 0.0 + 15.6x + x2 = 0 + -7.6 15.6x + x2 = 0 + -7.6 Combine like terms: 0 + -7.6 = -7.6 15.6x + x2 = -7.6 The x term is 15.6x. Take half its coefficient (7.8). Square it (60.84) and add it to both sides. Add '60.84' to each side of the equation. 15.6x + 60.84 + x2 = -7.6 + 60.84 Reorder the terms: 60.84 + 15.6x + x2 = -7.6 + 60.84 Combine like terms: -7.6 + 60.84 = 53.24 60.84 + 15.6x + x2 = 53.24 Factor a perfect square on the left side: (x + 7.8)(x + 7.8) = 53.24 Calculate the square root of the right side: 7.296574539 Break this problem into two subproblems by setting (x + 7.8) equal to 7.296574539 and -7.296574539.Subproblem 1
x + 7.8 = 7.296574539 Simplifying x + 7.8 = 7.296574539 Reorder the terms: 7.8 + x = 7.296574539 Solving 7.8 + x = 7.296574539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.8' to each side of the equation. 7.8 + -7.8 + x = 7.296574539 + -7.8 Combine like terms: 7.8 + -7.8 = 0.0 0.0 + x = 7.296574539 + -7.8 x = 7.296574539 + -7.8 Combine like terms: 7.296574539 + -7.8 = -0.503425461 x = -0.503425461 Simplifying x = -0.503425461Subproblem 2
x + 7.8 = -7.296574539 Simplifying x + 7.8 = -7.296574539 Reorder the terms: 7.8 + x = -7.296574539 Solving 7.8 + x = -7.296574539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.8' to each side of the equation. 7.8 + -7.8 + x = -7.296574539 + -7.8 Combine like terms: 7.8 + -7.8 = 0.0 0.0 + x = -7.296574539 + -7.8 x = -7.296574539 + -7.8 Combine like terms: -7.296574539 + -7.8 = -15.096574539 x = -15.096574539 Simplifying x = -15.096574539Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.503425461, -15.096574539}
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