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Simplifying 5x2 = 19x + -17 Reorder the terms: 5x2 = -17 + 19x Solving 5x2 = -17 + 19x Solving for variable 'x'. Reorder the terms: 17 + -19x + 5x2 = -17 + 19x + 17 + -19x Reorder the terms: 17 + -19x + 5x2 = -17 + 17 + 19x + -19x Combine like terms: -17 + 17 = 0 17 + -19x + 5x2 = 0 + 19x + -19x 17 + -19x + 5x2 = 19x + -19x Combine like terms: 19x + -19x = 0 17 + -19x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3.4 + -3.8x + x2 = 0 Move the constant term to the right: Add '-3.4' to each side of the equation. 3.4 + -3.8x + -3.4 + x2 = 0 + -3.4 Reorder the terms: 3.4 + -3.4 + -3.8x + x2 = 0 + -3.4 Combine like terms: 3.4 + -3.4 = 0.0 0.0 + -3.8x + x2 = 0 + -3.4 -3.8x + x2 = 0 + -3.4 Combine like terms: 0 + -3.4 = -3.4 -3.8x + x2 = -3.4 The x term is -3.8x. Take half its coefficient (-1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. -3.8x + 3.61 + x2 = -3.4 + 3.61 Reorder the terms: 3.61 + -3.8x + x2 = -3.4 + 3.61 Combine like terms: -3.4 + 3.61 = 0.21 3.61 + -3.8x + x2 = 0.21 Factor a perfect square on the left side: (x + -1.9)(x + -1.9) = 0.21 Calculate the square root of the right side: 0.458257569 Break this problem into two subproblems by setting (x + -1.9) equal to 0.458257569 and -0.458257569.Subproblem 1
x + -1.9 = 0.458257569 Simplifying x + -1.9 = 0.458257569 Reorder the terms: -1.9 + x = 0.458257569 Solving -1.9 + x = 0.458257569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9' to each side of the equation. -1.9 + 1.9 + x = 0.458257569 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + x = 0.458257569 + 1.9 x = 0.458257569 + 1.9 Combine like terms: 0.458257569 + 1.9 = 2.358257569 x = 2.358257569 Simplifying x = 2.358257569Subproblem 2
x + -1.9 = -0.458257569 Simplifying x + -1.9 = -0.458257569 Reorder the terms: -1.9 + x = -0.458257569 Solving -1.9 + x = -0.458257569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9' to each side of the equation. -1.9 + 1.9 + x = -0.458257569 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + x = -0.458257569 + 1.9 x = -0.458257569 + 1.9 Combine like terms: -0.458257569 + 1.9 = 1.441742431 x = 1.441742431 Simplifying x = 1.441742431Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.358257569, 1.441742431}
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