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Simplifying 0.75x2 + 1100x + -350 = 0 Reorder the terms: -350 + 1100x + 0.75x2 = 0 Solving -350 + 1100x + 0.75x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.75 the coefficient of the squared term: Divide each side by '0.75'. -466.6666667 + 1466.666667x + x2 = 0 Move the constant term to the right: Add '466.6666667' to each side of the equation. -466.6666667 + 1466.666667x + 466.6666667 + x2 = 0 + 466.6666667 Reorder the terms: -466.6666667 + 466.6666667 + 1466.666667x + x2 = 0 + 466.6666667 Combine like terms: -466.6666667 + 466.6666667 = 0.0000000 0.0000000 + 1466.666667x + x2 = 0 + 466.6666667 1466.666667x + x2 = 0 + 466.6666667 Combine like terms: 0 + 466.6666667 = 466.6666667 1466.666667x + x2 = 466.6666667 The x term is 1466.666667x. Take half its coefficient (733.3333335). Square it (537777.7780) and add it to both sides. Add '537777.7780' to each side of the equation. 1466.666667x + 537777.7780 + x2 = 466.6666667 + 537777.7780 Reorder the terms: 537777.7780 + 1466.666667x + x2 = 466.6666667 + 537777.7780 Combine like terms: 466.6666667 + 537777.7780 = 538244.4446667 537777.7780 + 1466.666667x + x2 = 538244.4446667 Factor a perfect square on the left side: (x + 733.3333335)(x + 733.3333335) = 538244.4446667 Calculate the square root of the right side: 733.651446306 Break this problem into two subproblems by setting (x + 733.3333335) equal to 733.651446306 and -733.651446306.Subproblem 1
x + 733.3333335 = 733.651446306 Simplifying x + 733.3333335 = 733.651446306 Reorder the terms: 733.3333335 + x = 733.651446306 Solving 733.3333335 + x = 733.651446306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-733.3333335' to each side of the equation. 733.3333335 + -733.3333335 + x = 733.651446306 + -733.3333335 Combine like terms: 733.3333335 + -733.3333335 = 0.0000000 0.0000000 + x = 733.651446306 + -733.3333335 x = 733.651446306 + -733.3333335 Combine like terms: 733.651446306 + -733.3333335 = 0.318112806 x = 0.318112806 Simplifying x = 0.318112806Subproblem 2
x + 733.3333335 = -733.651446306 Simplifying x + 733.3333335 = -733.651446306 Reorder the terms: 733.3333335 + x = -733.651446306 Solving 733.3333335 + x = -733.651446306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-733.3333335' to each side of the equation. 733.3333335 + -733.3333335 + x = -733.651446306 + -733.3333335 Combine like terms: 733.3333335 + -733.3333335 = 0.0000000 0.0000000 + x = -733.651446306 + -733.3333335 x = -733.651446306 + -733.3333335 Combine like terms: -733.651446306 + -733.3333335 = -1466.984779806 x = -1466.984779806 Simplifying x = -1466.984779806Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.318112806, -1466.984779806}
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