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Simplifying 5x2 = 17x + 19 Reorder the terms: 5x2 = 19 + 17x Solving 5x2 = 19 + 17x Solving for variable 'x'. Reorder the terms: -19 + -17x + 5x2 = 19 + 17x + -19 + -17x Reorder the terms: -19 + -17x + 5x2 = 19 + -19 + 17x + -17x Combine like terms: 19 + -19 = 0 -19 + -17x + 5x2 = 0 + 17x + -17x -19 + -17x + 5x2 = 17x + -17x Combine like terms: 17x + -17x = 0 -19 + -17x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.8 + -3.4x + x2 = 0 Move the constant term to the right: Add '3.8' to each side of the equation. -3.8 + -3.4x + 3.8 + x2 = 0 + 3.8 Reorder the terms: -3.8 + 3.8 + -3.4x + x2 = 0 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + -3.4x + x2 = 0 + 3.8 -3.4x + x2 = 0 + 3.8 Combine like terms: 0 + 3.8 = 3.8 -3.4x + x2 = 3.8 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 = 3.8 + 2.89 Reorder the terms: 2.89 + -3.4x + x2 = 3.8 + 2.89 Combine like terms: 3.8 + 2.89 = 6.69 2.89 + -3.4x + x2 = 6.69 Factor a perfect square on the left side: (x + -1.7)(x + -1.7) = 6.69 Calculate the square root of the right side: 2.586503431 Break this problem into two subproblems by setting (x + -1.7) equal to 2.586503431 and -2.586503431.Subproblem 1
x + -1.7 = 2.586503431 Simplifying x + -1.7 = 2.586503431 Reorder the terms: -1.7 + x = 2.586503431 Solving -1.7 + x = 2.586503431 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 = 2.586503431 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = 2.586503431 + 1.7 x = 2.586503431 + 1.7 Combine like terms: 2.586503431 + 1.7 = 4.286503431 x = 4.286503431 Simplifying x = 4.286503431Subproblem 2
x + -1.7 = -2.586503431 Simplifying x + -1.7 = -2.586503431 Reorder the terms: -1.7 + x = -2.586503431 Solving -1.7 + x = -2.586503431 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 = -2.586503431 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = -2.586503431 + 1.7 x = -2.586503431 + 1.7 Combine like terms: -2.586503431 + 1.7 = -0.886503431 x = -0.886503431 Simplifying x = -0.886503431Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.286503431, -0.886503431}
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