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Simplifying 2x2 + 43x + -50 = 15002 Reorder the terms: -50 + 43x + 2x2 = 15002 Solving -50 + 43x + 2x2 = 15002 Solving for variable 'x'. Reorder the terms: -50 + -15002 + 43x + 2x2 = 15002 + -15002 Combine like terms: -50 + -15002 = -15052 -15052 + 43x + 2x2 = 15002 + -15002 Combine like terms: 15002 + -15002 = 0 -15052 + 43x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7526 + 21.5x + x2 = 0 Move the constant term to the right: Add '7526' to each side of the equation. -7526 + 21.5x + 7526 + x2 = 0 + 7526 Reorder the terms: -7526 + 7526 + 21.5x + x2 = 0 + 7526 Combine like terms: -7526 + 7526 = 0 0 + 21.5x + x2 = 0 + 7526 21.5x + x2 = 0 + 7526 Combine like terms: 0 + 7526 = 7526 21.5x + x2 = 7526 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 = 7526 + 115.5625 Reorder the terms: 115.5625 + 21.5x + x2 = 7526 + 115.5625 Combine like terms: 7526 + 115.5625 = 7641.5625 115.5625 + 21.5x + x2 = 7641.5625 Factor a perfect square on the left side: (x + 10.75)(x + 10.75) = 7641.5625 Calculate the square root of the right side: 87.416031138 Break this problem into two subproblems by setting (x + 10.75) equal to 87.416031138 and -87.416031138.Subproblem 1
x + 10.75 = 87.416031138 Simplifying x + 10.75 = 87.416031138 Reorder the terms: 10.75 + x = 87.416031138 Solving 10.75 + x = 87.416031138 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 = 87.416031138 + -10.75 Combine like terms: 10.75 + -10.75 = 0.00 0.00 + x = 87.416031138 + -10.75 x = 87.416031138 + -10.75 Combine like terms: 87.416031138 + -10.75 = 76.666031138 x = 76.666031138 Simplifying x = 76.666031138Subproblem 2
x + 10.75 = -87.416031138 Simplifying x + 10.75 = -87.416031138 Reorder the terms: 10.75 + x = -87.416031138 Solving 10.75 + x = -87.416031138 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 = -87.416031138 + -10.75 Combine like terms: 10.75 + -10.75 = 0.00 0.00 + x = -87.416031138 + -10.75 x = -87.416031138 + -10.75 Combine like terms: -87.416031138 + -10.75 = -98.166031138 x = -98.166031138 Simplifying x = -98.166031138Solution
The solution to the problem is based on the solutions from the subproblems. x = {76.666031138, -98.166031138}
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