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Simplifying 5x2 + -39x + -100 = 0 Reorder the terms: -100 + -39x + 5x2 = 0 Solving -100 + -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'. -20 + -7.8x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -7.8x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -7.8x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -7.8x + x2 = 0 + 20 -7.8x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -7.8x + x2 = 20 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 = 20 + 15.21 Reorder the terms: 15.21 + -7.8x + x2 = 20 + 15.21 Combine like terms: 20 + 15.21 = 35.21 15.21 + -7.8x + x2 = 35.21 Factor a perfect square on the left side: (x + -3.9)(x + -3.9) = 35.21 Calculate the square root of the right side: 5.93380148 Break this problem into two subproblems by setting (x + -3.9) equal to 5.93380148 and -5.93380148.Subproblem 1
x + -3.9 = 5.93380148 Simplifying x + -3.9 = 5.93380148 Reorder the terms: -3.9 + x = 5.93380148 Solving -3.9 + x = 5.93380148 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 = 5.93380148 + 3.9 Combine like terms: -3.9 + 3.9 = 0.0 0.0 + x = 5.93380148 + 3.9 x = 5.93380148 + 3.9 Combine like terms: 5.93380148 + 3.9 = 9.83380148 x = 9.83380148 Simplifying x = 9.83380148Subproblem 2
x + -3.9 = -5.93380148 Simplifying x + -3.9 = -5.93380148 Reorder the terms: -3.9 + x = -5.93380148 Solving -3.9 + x = -5.93380148 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 = -5.93380148 + 3.9 Combine like terms: -3.9 + 3.9 = 0.0 0.0 + x = -5.93380148 + 3.9 x = -5.93380148 + 3.9 Combine like terms: -5.93380148 + 3.9 = -2.03380148 x = -2.03380148 Simplifying x = -2.03380148Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.83380148, -2.03380148}
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