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Simplifying 2x2 + 43x + -175 = 10 Reorder the terms: -175 + 43x + 2x2 = 10 Solving -175 + 43x + 2x2 = 10 Solving for variable 'x'. Reorder the terms: -175 + -10 + 43x + 2x2 = 10 + -10 Combine like terms: -175 + -10 = -185 -185 + 43x + 2x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -185 + 43x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -92.5 + 21.5x + x2 = 0 Move the constant term to the right: Add '92.5' to each side of the equation. -92.5 + 21.5x + 92.5 + x2 = 0 + 92.5 Reorder the terms: -92.5 + 92.5 + 21.5x + x2 = 0 + 92.5 Combine like terms: -92.5 + 92.5 = 0.0 0.0 + 21.5x + x2 = 0 + 92.5 21.5x + x2 = 0 + 92.5 Combine like terms: 0 + 92.5 = 92.5 21.5x + x2 = 92.5 The x term is 21.5x. Take half its coefficient (10.75). Square it (115.5625) and add it to both sides. Add '115.5625' to each side of the equation. 21.5x + 115.5625 + x2 = 92.5 + 115.5625 Reorder the terms: 115.5625 + 21.5x + x2 = 92.5 + 115.5625 Combine like terms: 92.5 + 115.5625 = 208.0625 115.5625 + 21.5x + x2 = 208.0625 Factor a perfect square on the left side: (x + 10.75)(x + 10.75) = 208.0625 Calculate the square root of the right side: 14.424371737 Break this problem into two subproblems by setting (x + 10.75) equal to 14.424371737 and -14.424371737.Subproblem 1
x + 10.75 = 14.424371737 Simplifying x + 10.75 = 14.424371737 Reorder the terms: 10.75 + x = 14.424371737 Solving 10.75 + x = 14.424371737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.75' to each side of the equation. 10.75 + -10.75 + x = 14.424371737 + -10.75 Combine like terms: 10.75 + -10.75 = 0.00 0.00 + x = 14.424371737 + -10.75 x = 14.424371737 + -10.75 Combine like terms: 14.424371737 + -10.75 = 3.674371737 x = 3.674371737 Simplifying x = 3.674371737Subproblem 2
x + 10.75 = -14.424371737 Simplifying x + 10.75 = -14.424371737 Reorder the terms: 10.75 + x = -14.424371737 Solving 10.75 + x = -14.424371737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.75' to each side of the equation. 10.75 + -10.75 + x = -14.424371737 + -10.75 Combine like terms: 10.75 + -10.75 = 0.00 0.00 + x = -14.424371737 + -10.75 x = -14.424371737 + -10.75 Combine like terms: -14.424371737 + -10.75 = -25.174371737 x = -25.174371737 Simplifying x = -25.174371737Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.674371737, -25.174371737}
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