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Simplifying 0.5x2 + 0.84x + -0.105 = 0 Reorder the terms: -0.105 + 0.84x + 0.5x2 = 0 Solving -0.105 + 0.84x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -0.21 + 1.68x + x2 = 0 Move the constant term to the right: Add '0.21' to each side of the equation. -0.21 + 1.68x + 0.21 + x2 = 0 + 0.21 Reorder the terms: -0.21 + 0.21 + 1.68x + x2 = 0 + 0.21 Combine like terms: -0.21 + 0.21 = 0.00 0.00 + 1.68x + x2 = 0 + 0.21 1.68x + x2 = 0 + 0.21 Combine like terms: 0 + 0.21 = 0.21 1.68x + x2 = 0.21 The x term is 1.68x. Take half its coefficient (0.84). Square it (0.7056) and add it to both sides. Add '0.7056' to each side of the equation. 1.68x + 0.7056 + x2 = 0.21 + 0.7056 Reorder the terms: 0.7056 + 1.68x + x2 = 0.21 + 0.7056 Combine like terms: 0.21 + 0.7056 = 0.9156 0.7056 + 1.68x + x2 = 0.9156 Factor a perfect square on the left side: (x + 0.84)(x + 0.84) = 0.9156 Calculate the square root of the right side: 0.956869897 Break this problem into two subproblems by setting (x + 0.84) equal to 0.956869897 and -0.956869897.Subproblem 1
x + 0.84 = 0.956869897 Simplifying x + 0.84 = 0.956869897 Reorder the terms: 0.84 + x = 0.956869897 Solving 0.84 + x = 0.956869897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.84' to each side of the equation. 0.84 + -0.84 + x = 0.956869897 + -0.84 Combine like terms: 0.84 + -0.84 = 0.00 0.00 + x = 0.956869897 + -0.84 x = 0.956869897 + -0.84 Combine like terms: 0.956869897 + -0.84 = 0.116869897 x = 0.116869897 Simplifying x = 0.116869897Subproblem 2
x + 0.84 = -0.956869897 Simplifying x + 0.84 = -0.956869897 Reorder the terms: 0.84 + x = -0.956869897 Solving 0.84 + x = -0.956869897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.84' to each side of the equation. 0.84 + -0.84 + x = -0.956869897 + -0.84 Combine like terms: 0.84 + -0.84 = 0.00 0.00 + x = -0.956869897 + -0.84 x = -0.956869897 + -0.84 Combine like terms: -0.956869897 + -0.84 = -1.796869897 x = -1.796869897 Simplifying x = -1.796869897Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.116869897, -1.796869897}
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