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Simplifying 2x2 + 2x + -370 = 5x + 1 Reorder the terms: -370 + 2x + 2x2 = 5x + 1 Reorder the terms: -370 + 2x + 2x2 = 1 + 5x Solving -370 + 2x + 2x2 = 1 + 5x Solving for variable 'x'. Reorder the terms: -370 + -1 + 2x + -5x + 2x2 = 1 + 5x + -1 + -5x Combine like terms: -370 + -1 = -371 -371 + 2x + -5x + 2x2 = 1 + 5x + -1 + -5x Combine like terms: 2x + -5x = -3x -371 + -3x + 2x2 = 1 + 5x + -1 + -5x Reorder the terms: -371 + -3x + 2x2 = 1 + -1 + 5x + -5x Combine like terms: 1 + -1 = 0 -371 + -3x + 2x2 = 0 + 5x + -5x -371 + -3x + 2x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -371 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -185.5 + -1.5x + x2 = 0 Move the constant term to the right: Add '185.5' to each side of the equation. -185.5 + -1.5x + 185.5 + x2 = 0 + 185.5 Reorder the terms: -185.5 + 185.5 + -1.5x + x2 = 0 + 185.5 Combine like terms: -185.5 + 185.5 = 0.0 0.0 + -1.5x + x2 = 0 + 185.5 -1.5x + x2 = 0 + 185.5 Combine like terms: 0 + 185.5 = 185.5 -1.5x + x2 = 185.5 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 185.5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 185.5 + 0.5625 Combine like terms: 185.5 + 0.5625 = 186.0625 0.5625 + -1.5x + x2 = 186.0625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 186.0625 Calculate the square root of the right side: 13.640472866 Break this problem into two subproblems by setting (x + -0.75) equal to 13.640472866 and -13.640472866.Subproblem 1
x + -0.75 = 13.640472866 Simplifying x + -0.75 = 13.640472866 Reorder the terms: -0.75 + x = 13.640472866 Solving -0.75 + x = 13.640472866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 13.640472866 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 13.640472866 + 0.75 x = 13.640472866 + 0.75 Combine like terms: 13.640472866 + 0.75 = 14.390472866 x = 14.390472866 Simplifying x = 14.390472866Subproblem 2
x + -0.75 = -13.640472866 Simplifying x + -0.75 = -13.640472866 Reorder the terms: -0.75 + x = -13.640472866 Solving -0.75 + x = -13.640472866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -13.640472866 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -13.640472866 + 0.75 x = -13.640472866 + 0.75 Combine like terms: -13.640472866 + 0.75 = -12.890472866 x = -12.890472866 Simplifying x = -12.890472866Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.390472866, -12.890472866}
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