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Simplifying 5x2 + 1999x + 8 = 0 Reorder the terms: 8 + 1999x + 5x2 = 0 Solving 8 + 1999x + 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 + 399.8x + x2 = 0 Move the constant term to the right: Add '-1.6' to each side of the equation. 1.6 + 399.8x + -1.6 + x2 = 0 + -1.6 Reorder the terms: 1.6 + -1.6 + 399.8x + x2 = 0 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + 399.8x + x2 = 0 + -1.6 399.8x + x2 = 0 + -1.6 Combine like terms: 0 + -1.6 = -1.6 399.8x + x2 = -1.6 The x term is 399.8x. Take half its coefficient (199.9). Square it (39960.01) and add it to both sides. Add '39960.01' to each side of the equation. 399.8x + 39960.01 + x2 = -1.6 + 39960.01 Reorder the terms: 39960.01 + 399.8x + x2 = -1.6 + 39960.01 Combine like terms: -1.6 + 39960.01 = 39958.41 39960.01 + 399.8x + x2 = 39958.41 Factor a perfect square on the left side: (x + 199.9)(x + 199.9) = 39958.41 Calculate the square root of the right side: 199.895997959 Break this problem into two subproblems by setting (x + 199.9) equal to 199.895997959 and -199.895997959.Subproblem 1
x + 199.9 = 199.895997959 Simplifying x + 199.9 = 199.895997959 Reorder the terms: 199.9 + x = 199.895997959 Solving 199.9 + x = 199.895997959 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-199.9' to each side of the equation. 199.9 + -199.9 + x = 199.895997959 + -199.9 Combine like terms: 199.9 + -199.9 = 0.0 0.0 + x = 199.895997959 + -199.9 x = 199.895997959 + -199.9 Combine like terms: 199.895997959 + -199.9 = -0.004002041 x = -0.004002041 Simplifying x = -0.004002041Subproblem 2
x + 199.9 = -199.895997959 Simplifying x + 199.9 = -199.895997959 Reorder the terms: 199.9 + x = -199.895997959 Solving 199.9 + x = -199.895997959 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-199.9' to each side of the equation. 199.9 + -199.9 + x = -199.895997959 + -199.9 Combine like terms: 199.9 + -199.9 = 0.0 0.0 + x = -199.895997959 + -199.9 x = -199.895997959 + -199.9 Combine like terms: -199.895997959 + -199.9 = -399.795997959 x = -399.795997959 Simplifying x = -399.795997959Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.004002041, -399.795997959}
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