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Simplifying 5x2 = 17x + -2 Reorder the terms: 5x2 = -2 + 17x Solving 5x2 = -2 + 17x Solving for variable 'x'. Reorder the terms: 2 + -17x + 5x2 = -2 + 17x + 2 + -17x Reorder the terms: 2 + -17x + 5x2 = -2 + 2 + 17x + -17x Combine like terms: -2 + 2 = 0 2 + -17x + 5x2 = 0 + 17x + -17x 2 + -17x + 5x2 = 17x + -17x Combine like terms: 17x + -17x = 0 2 + -17x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + -3.4x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -3.4x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -3.4x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -3.4x + x2 = 0 + -0.4 -3.4x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -3.4x + x2 = -0.4 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 = -0.4 + 2.89 Reorder the terms: 2.89 + -3.4x + x2 = -0.4 + 2.89 Combine like terms: -0.4 + 2.89 = 2.49 2.89 + -3.4x + x2 = 2.49 Factor a perfect square on the left side: (x + -1.7)(x + -1.7) = 2.49 Calculate the square root of the right side: 1.577973384 Break this problem into two subproblems by setting (x + -1.7) equal to 1.577973384 and -1.577973384.Subproblem 1
x + -1.7 = 1.577973384 Simplifying x + -1.7 = 1.577973384 Reorder the terms: -1.7 + x = 1.577973384 Solving -1.7 + x = 1.577973384 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 = 1.577973384 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = 1.577973384 + 1.7 x = 1.577973384 + 1.7 Combine like terms: 1.577973384 + 1.7 = 3.277973384 x = 3.277973384 Simplifying x = 3.277973384Subproblem 2
x + -1.7 = -1.577973384 Simplifying x + -1.7 = -1.577973384 Reorder the terms: -1.7 + x = -1.577973384 Solving -1.7 + x = -1.577973384 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 = -1.577973384 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = -1.577973384 + 1.7 x = -1.577973384 + 1.7 Combine like terms: -1.577973384 + 1.7 = 0.122026616 x = 0.122026616 Simplifying x = 0.122026616Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.277973384, 0.122026616}
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