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Simplifying 5x2 + -11x = 6x + 3 Reorder the terms: -11x + 5x2 = 6x + 3 Reorder the terms: -11x + 5x2 = 3 + 6x Solving -11x + 5x2 = 3 + 6x Solving for variable 'x'. Reorder the terms: -3 + -11x + -6x + 5x2 = 3 + 6x + -3 + -6x Combine like terms: -11x + -6x = -17x -3 + -17x + 5x2 = 3 + 6x + -3 + -6x Reorder the terms: -3 + -17x + 5x2 = 3 + -3 + 6x + -6x Combine like terms: 3 + -3 = 0 -3 + -17x + 5x2 = 0 + 6x + -6x -3 + -17x + 5x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -3 + -17x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + -3.4x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -3.4x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -3.4x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -3.4x + x2 = 0 + 0.6 -3.4x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -3.4x + x2 = 0.6 The x term is -3.4x. Take half its coefficient (-1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. -3.4x + 2.89 + x2 = 0.6 + 2.89 Reorder the terms: 2.89 + -3.4x + x2 = 0.6 + 2.89 Combine like terms: 0.6 + 2.89 = 3.49 2.89 + -3.4x + x2 = 3.49 Factor a perfect square on the left side: (x + -1.7)(x + -1.7) = 3.49 Calculate the square root of the right side: 1.868154169 Break this problem into two subproblems by setting (x + -1.7) equal to 1.868154169 and -1.868154169.Subproblem 1
x + -1.7 = 1.868154169 Simplifying x + -1.7 = 1.868154169 Reorder the terms: -1.7 + x = 1.868154169 Solving -1.7 + x = 1.868154169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + x = 1.868154169 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = 1.868154169 + 1.7 x = 1.868154169 + 1.7 Combine like terms: 1.868154169 + 1.7 = 3.568154169 x = 3.568154169 Simplifying x = 3.568154169Subproblem 2
x + -1.7 = -1.868154169 Simplifying x + -1.7 = -1.868154169 Reorder the terms: -1.7 + x = -1.868154169 Solving -1.7 + x = -1.868154169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + x = -1.868154169 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = -1.868154169 + 1.7 x = -1.868154169 + 1.7 Combine like terms: -1.868154169 + 1.7 = -0.168154169 x = -0.168154169 Simplifying x = -0.168154169Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.568154169, -0.168154169}
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