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Simplifying 4x2 + 135x + 1000 = 0 Reorder the terms: 1000 + 135x + 4x2 = 0 Solving 1000 + 135x + 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'. 250 + 33.75x + x2 = 0 Move the constant term to the right: Add '-250' to each side of the equation. 250 + 33.75x + -250 + x2 = 0 + -250 Reorder the terms: 250 + -250 + 33.75x + x2 = 0 + -250 Combine like terms: 250 + -250 = 0 0 + 33.75x + x2 = 0 + -250 33.75x + x2 = 0 + -250 Combine like terms: 0 + -250 = -250 33.75x + x2 = -250 The x term is 33.75x. Take half its coefficient (16.875). Square it (284.765625) and add it to both sides. Add '284.765625' to each side of the equation. 33.75x + 284.765625 + x2 = -250 + 284.765625 Reorder the terms: 284.765625 + 33.75x + x2 = -250 + 284.765625 Combine like terms: -250 + 284.765625 = 34.765625 284.765625 + 33.75x + x2 = 34.765625 Factor a perfect square on the left side: (x + 16.875)(x + 16.875) = 34.765625 Calculate the square root of the right side: 5.896238208 Break this problem into two subproblems by setting (x + 16.875) equal to 5.896238208 and -5.896238208.Subproblem 1
x + 16.875 = 5.896238208 Simplifying x + 16.875 = 5.896238208 Reorder the terms: 16.875 + x = 5.896238208 Solving 16.875 + x = 5.896238208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.875' to each side of the equation. 16.875 + -16.875 + x = 5.896238208 + -16.875 Combine like terms: 16.875 + -16.875 = 0.000 0.000 + x = 5.896238208 + -16.875 x = 5.896238208 + -16.875 Combine like terms: 5.896238208 + -16.875 = -10.978761792 x = -10.978761792 Simplifying x = -10.978761792Subproblem 2
x + 16.875 = -5.896238208 Simplifying x + 16.875 = -5.896238208 Reorder the terms: 16.875 + x = -5.896238208 Solving 16.875 + x = -5.896238208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.875' to each side of the equation. 16.875 + -16.875 + x = -5.896238208 + -16.875 Combine like terms: 16.875 + -16.875 = 0.000 0.000 + x = -5.896238208 + -16.875 x = -5.896238208 + -16.875 Combine like terms: -5.896238208 + -16.875 = -22.771238208 x = -22.771238208 Simplifying x = -22.771238208Solution
The solution to the problem is based on the solutions from the subproblems. x = {-10.978761792, -22.771238208}
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