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Simplifying 5x2 + 39x + 60 = 0 Reorder the terms: 60 + 39x + 5x2 = 0 Solving 60 + 39x + 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'. 12 + 7.8x + x2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + 7.8x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + 7.8x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 7.8x + x2 = 0 + -12 7.8x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 7.8x + x2 = -12 The x term is 7.8x. Take half its coefficient (3.9). Square it (15.21) and add it to both sides. Add '15.21' to each side of the equation. 7.8x + 15.21 + x2 = -12 + 15.21 Reorder the terms: 15.21 + 7.8x + x2 = -12 + 15.21 Combine like terms: -12 + 15.21 = 3.21 15.21 + 7.8x + x2 = 3.21 Factor a perfect square on the left side: (x + 3.9)(x + 3.9) = 3.21 Calculate the square root of the right side: 1.791647287 Break this problem into two subproblems by setting (x + 3.9) equal to 1.791647287 and -1.791647287.Subproblem 1
x + 3.9 = 1.791647287 Simplifying x + 3.9 = 1.791647287 Reorder the terms: 3.9 + x = 1.791647287 Solving 3.9 + x = 1.791647287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.9' to each side of the equation. 3.9 + -3.9 + x = 1.791647287 + -3.9 Combine like terms: 3.9 + -3.9 = 0.0 0.0 + x = 1.791647287 + -3.9 x = 1.791647287 + -3.9 Combine like terms: 1.791647287 + -3.9 = -2.108352713 x = -2.108352713 Simplifying x = -2.108352713Subproblem 2
x + 3.9 = -1.791647287 Simplifying x + 3.9 = -1.791647287 Reorder the terms: 3.9 + x = -1.791647287 Solving 3.9 + x = -1.791647287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.9' to each side of the equation. 3.9 + -3.9 + x = -1.791647287 + -3.9 Combine like terms: 3.9 + -3.9 = 0.0 0.0 + x = -1.791647287 + -3.9 x = -1.791647287 + -3.9 Combine like terms: -1.791647287 + -3.9 = -5.691647287 x = -5.691647287 Simplifying x = -5.691647287Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.108352713, -5.691647287}
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