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Simplifying 5x2 = 7x + 17 Reorder the terms: 5x2 = 17 + 7x Solving 5x2 = 17 + 7x Solving for variable 'x'. Reorder the terms: -17 + -7x + 5x2 = 17 + 7x + -17 + -7x Reorder the terms: -17 + -7x + 5x2 = 17 + -17 + 7x + -7x Combine like terms: 17 + -17 = 0 -17 + -7x + 5x2 = 0 + 7x + -7x -17 + -7x + 5x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -17 + -7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.4 + -1.4x + x2 = 0 Move the constant term to the right: Add '3.4' to each side of the equation. -3.4 + -1.4x + 3.4 + x2 = 0 + 3.4 Reorder the terms: -3.4 + 3.4 + -1.4x + x2 = 0 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + -1.4x + x2 = 0 + 3.4 -1.4x + x2 = 0 + 3.4 Combine like terms: 0 + 3.4 = 3.4 -1.4x + x2 = 3.4 The x term is -1.4x. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x + 0.49 + x2 = 3.4 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = 3.4 + 0.49 Combine like terms: 3.4 + 0.49 = 3.89 0.49 + -1.4x + x2 = 3.89 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 3.89 Calculate the square root of the right side: 1.972308292 Break this problem into two subproblems by setting (x + -0.7) equal to 1.972308292 and -1.972308292.Subproblem 1
x + -0.7 = 1.972308292 Simplifying x + -0.7 = 1.972308292 Reorder the terms: -0.7 + x = 1.972308292 Solving -0.7 + x = 1.972308292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 1.972308292 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 1.972308292 + 0.7 x = 1.972308292 + 0.7 Combine like terms: 1.972308292 + 0.7 = 2.672308292 x = 2.672308292 Simplifying x = 2.672308292Subproblem 2
x + -0.7 = -1.972308292 Simplifying x + -0.7 = -1.972308292 Reorder the terms: -0.7 + x = -1.972308292 Solving -0.7 + x = -1.972308292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = -1.972308292 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -1.972308292 + 0.7 x = -1.972308292 + 0.7 Combine like terms: -1.972308292 + 0.7 = -1.272308292 x = -1.272308292 Simplifying x = -1.272308292Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.672308292, -1.272308292}
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