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Simplifying 5x2 + 19x + -101 = 0 Reorder the terms: -101 + 19x + 5x2 = 0 Solving -101 + 19x + 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'. -20.2 + 3.8x + x2 = 0 Move the constant term to the right: Add '20.2' to each side of the equation. -20.2 + 3.8x + 20.2 + x2 = 0 + 20.2 Reorder the terms: -20.2 + 20.2 + 3.8x + x2 = 0 + 20.2 Combine like terms: -20.2 + 20.2 = 0.0 0.0 + 3.8x + x2 = 0 + 20.2 3.8x + x2 = 0 + 20.2 Combine like terms: 0 + 20.2 = 20.2 3.8x + x2 = 20.2 The x term is 3.8x. Take half its coefficient (1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. 3.8x + 3.61 + x2 = 20.2 + 3.61 Reorder the terms: 3.61 + 3.8x + x2 = 20.2 + 3.61 Combine like terms: 20.2 + 3.61 = 23.81 3.61 + 3.8x + x2 = 23.81 Factor a perfect square on the left side: (x + 1.9)(x + 1.9) = 23.81 Calculate the square root of the right side: 4.87954916 Break this problem into two subproblems by setting (x + 1.9) equal to 4.87954916 and -4.87954916.Subproblem 1
x + 1.9 = 4.87954916 Simplifying x + 1.9 = 4.87954916 Reorder the terms: 1.9 + x = 4.87954916 Solving 1.9 + x = 4.87954916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + x = 4.87954916 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = 4.87954916 + -1.9 x = 4.87954916 + -1.9 Combine like terms: 4.87954916 + -1.9 = 2.97954916 x = 2.97954916 Simplifying x = 2.97954916Subproblem 2
x + 1.9 = -4.87954916 Simplifying x + 1.9 = -4.87954916 Reorder the terms: 1.9 + x = -4.87954916 Solving 1.9 + x = -4.87954916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + x = -4.87954916 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = -4.87954916 + -1.9 x = -4.87954916 + -1.9 Combine like terms: -4.87954916 + -1.9 = -6.77954916 x = -6.77954916 Simplifying x = -6.77954916Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.97954916, -6.77954916}
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