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Simplifying 5x2 + -39x + 8 = 0 Reorder the terms: 8 + -39x + 5x2 = 0 Solving 8 + -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'. 1.6 + -7.8x + x2 = 0 Move the constant term to the right: Add '-1.6' to each side of the equation. 1.6 + -7.8x + -1.6 + x2 = 0 + -1.6 Reorder the terms: 1.6 + -1.6 + -7.8x + x2 = 0 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + -7.8x + x2 = 0 + -1.6 -7.8x + x2 = 0 + -1.6 Combine like terms: 0 + -1.6 = -1.6 -7.8x + x2 = -1.6 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 = -1.6 + 15.21 Reorder the terms: 15.21 + -7.8x + x2 = -1.6 + 15.21 Combine like terms: -1.6 + 15.21 = 13.61 15.21 + -7.8x + x2 = 13.61 Factor a perfect square on the left side: (x + -3.9)(x + -3.9) = 13.61 Calculate the square root of the right side: 3.689173349 Break this problem into two subproblems by setting (x + -3.9) equal to 3.689173349 and -3.689173349.Subproblem 1
x + -3.9 = 3.689173349 Simplifying x + -3.9 = 3.689173349 Reorder the terms: -3.9 + x = 3.689173349 Solving -3.9 + x = 3.689173349 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 = 3.689173349 + 3.9 Combine like terms: -3.9 + 3.9 = 0.0 0.0 + x = 3.689173349 + 3.9 x = 3.689173349 + 3.9 Combine like terms: 3.689173349 + 3.9 = 7.589173349 x = 7.589173349 Simplifying x = 7.589173349Subproblem 2
x + -3.9 = -3.689173349 Simplifying x + -3.9 = -3.689173349 Reorder the terms: -3.9 + x = -3.689173349 Solving -3.9 + x = -3.689173349 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 = -3.689173349 + 3.9 Combine like terms: -3.9 + 3.9 = 0.0 0.0 + x = -3.689173349 + 3.9 x = -3.689173349 + 3.9 Combine like terms: -3.689173349 + 3.9 = 0.210826651 x = 0.210826651 Simplifying x = 0.210826651Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.589173349, 0.210826651}
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