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Simplifying 20x2 + x + -39 = 0 Reorder the terms: -39 + x + 20x2 = 0 Solving -39 + x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -1.95 + 0.05x + x2 = 0 Move the constant term to the right: Add '1.95' to each side of the equation. -1.95 + 0.05x + 1.95 + x2 = 0 + 1.95 Reorder the terms: -1.95 + 1.95 + 0.05x + x2 = 0 + 1.95 Combine like terms: -1.95 + 1.95 = 0.00 0.00 + 0.05x + x2 = 0 + 1.95 0.05x + x2 = 0 + 1.95 Combine like terms: 0 + 1.95 = 1.95 0.05x + x2 = 1.95 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.05x + 0.25 + x2 = 1.95 + 0.25 Reorder the terms: 0.25 + 0.05x + x2 = 1.95 + 0.25 Combine like terms: 1.95 + 0.25 = 2.2 0.25 + 0.05x + x2 = 2.2 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.2 Calculate the square root of the right side: 1.483239697 Break this problem into two subproblems by setting (x + 0.5) equal to 1.483239697 and -1.483239697.Subproblem 1
x + 0.5 = 1.483239697 Simplifying x + 0.5 = 1.483239697 Reorder the terms: 0.5 + x = 1.483239697 Solving 0.5 + x = 1.483239697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.483239697 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.483239697 + -0.5 x = 1.483239697 + -0.5 Combine like terms: 1.483239697 + -0.5 = 0.983239697 x = 0.983239697 Simplifying x = 0.983239697Subproblem 2
x + 0.5 = -1.483239697 Simplifying x + 0.5 = -1.483239697 Reorder the terms: 0.5 + x = -1.483239697 Solving 0.5 + x = -1.483239697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.483239697 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.483239697 + -0.5 x = -1.483239697 + -0.5 Combine like terms: -1.483239697 + -0.5 = -1.983239697 x = -1.983239697 Simplifying x = -1.983239697Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.983239697, -1.983239697}
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