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Simplifying 5x2 = 11x + 17 Reorder the terms: 5x2 = 17 + 11x Solving 5x2 = 17 + 11x Solving for variable 'x'. Reorder the terms: -17 + -11x + 5x2 = 17 + 11x + -17 + -11x Reorder the terms: -17 + -11x + 5x2 = 17 + -17 + 11x + -11x Combine like terms: 17 + -17 = 0 -17 + -11x + 5x2 = 0 + 11x + -11x -17 + -11x + 5x2 = 11x + -11x Combine like terms: 11x + -11x = 0 -17 + -11x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.4 + -2.2x + x2 = 0 Move the constant term to the right: Add '3.4' to each side of the equation. -3.4 + -2.2x + 3.4 + x2 = 0 + 3.4 Reorder the terms: -3.4 + 3.4 + -2.2x + x2 = 0 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + -2.2x + x2 = 0 + 3.4 -2.2x + x2 = 0 + 3.4 Combine like terms: 0 + 3.4 = 3.4 -2.2x + x2 = 3.4 The x term is -2.2x. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2x + 1.21 + x2 = 3.4 + 1.21 Reorder the terms: 1.21 + -2.2x + x2 = 3.4 + 1.21 Combine like terms: 3.4 + 1.21 = 4.61 1.21 + -2.2x + x2 = 4.61 Factor a perfect square on the left side: (x + -1.1)(x + -1.1) = 4.61 Calculate the square root of the right side: 2.147091055 Break this problem into two subproblems by setting (x + -1.1) equal to 2.147091055 and -2.147091055.Subproblem 1
x + -1.1 = 2.147091055 Simplifying x + -1.1 = 2.147091055 Reorder the terms: -1.1 + x = 2.147091055 Solving -1.1 + x = 2.147091055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = 2.147091055 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = 2.147091055 + 1.1 x = 2.147091055 + 1.1 Combine like terms: 2.147091055 + 1.1 = 3.247091055 x = 3.247091055 Simplifying x = 3.247091055Subproblem 2
x + -1.1 = -2.147091055 Simplifying x + -1.1 = -2.147091055 Reorder the terms: -1.1 + x = -2.147091055 Solving -1.1 + x = -2.147091055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = -2.147091055 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = -2.147091055 + 1.1 x = -2.147091055 + 1.1 Combine like terms: -2.147091055 + 1.1 = -1.047091055 x = -1.047091055 Simplifying x = -1.047091055Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.247091055, -1.047091055}
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