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Simplifying 4x2 + 94x + 3 = 0 Reorder the terms: 3 + 94x + 4x2 = 0 Solving 3 + 94x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + 23.5x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 23.5x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 23.5x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 23.5x + x2 = 0 + -0.75 23.5x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 23.5x + x2 = -0.75 The x term is 23.5x. Take half its coefficient (11.75). Square it (138.0625) and add it to both sides. Add '138.0625' to each side of the equation. 23.5x + 138.0625 + x2 = -0.75 + 138.0625 Reorder the terms: 138.0625 + 23.5x + x2 = -0.75 + 138.0625 Combine like terms: -0.75 + 138.0625 = 137.3125 138.0625 + 23.5x + x2 = 137.3125 Factor a perfect square on the left side: (x + 11.75)(x + 11.75) = 137.3125 Calculate the square root of the right side: 11.718041645 Break this problem into two subproblems by setting (x + 11.75) equal to 11.718041645 and -11.718041645.Subproblem 1
x + 11.75 = 11.718041645 Simplifying x + 11.75 = 11.718041645 Reorder the terms: 11.75 + x = 11.718041645 Solving 11.75 + x = 11.718041645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.75' to each side of the equation. 11.75 + -11.75 + x = 11.718041645 + -11.75 Combine like terms: 11.75 + -11.75 = 0.00 0.00 + x = 11.718041645 + -11.75 x = 11.718041645 + -11.75 Combine like terms: 11.718041645 + -11.75 = -0.031958355 x = -0.031958355 Simplifying x = -0.031958355Subproblem 2
x + 11.75 = -11.718041645 Simplifying x + 11.75 = -11.718041645 Reorder the terms: 11.75 + x = -11.718041645 Solving 11.75 + x = -11.718041645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.75' to each side of the equation. 11.75 + -11.75 + x = -11.718041645 + -11.75 Combine like terms: 11.75 + -11.75 = 0.00 0.00 + x = -11.718041645 + -11.75 x = -11.718041645 + -11.75 Combine like terms: -11.718041645 + -11.75 = -23.468041645 x = -23.468041645 Simplifying x = -23.468041645Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.031958355, -23.468041645}
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