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Simplifying 4x2 + -17x + 7 = 4x + 4x Reorder the terms: 7 + -17x + 4x2 = 4x + 4x Combine like terms: 4x + 4x = 8x 7 + -17x + 4x2 = 8x Solving 7 + -17x + 4x2 = 8x Solving for variable 'x'. Reorder the terms: 7 + -17x + -8x + 4x2 = 8x + -8x Combine like terms: -17x + -8x = -25x 7 + -25x + 4x2 = 8x + -8x Combine like terms: 8x + -8x = 0 7 + -25x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + -6.25x + x2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + -6.25x + -1.75 + x2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + -6.25x + x2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + -6.25x + x2 = 0 + -1.75 -6.25x + x2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 -6.25x + x2 = -1.75 The x term is -6.25x. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25x + 9.765625 + x2 = -1.75 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = -1.75 + 9.765625 Combine like terms: -1.75 + 9.765625 = 8.015625 9.765625 + -6.25x + x2 = 8.015625 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = 8.015625 Calculate the square root of the right side: 2.831187913 Break this problem into two subproblems by setting (x + -3.125) equal to 2.831187913 and -2.831187913.Subproblem 1
x + -3.125 = 2.831187913 Simplifying x + -3.125 = 2.831187913 Reorder the terms: -3.125 + x = 2.831187913 Solving -3.125 + x = 2.831187913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = 2.831187913 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 2.831187913 + 3.125 x = 2.831187913 + 3.125 Combine like terms: 2.831187913 + 3.125 = 5.956187913 x = 5.956187913 Simplifying x = 5.956187913Subproblem 2
x + -3.125 = -2.831187913 Simplifying x + -3.125 = -2.831187913 Reorder the terms: -3.125 + x = -2.831187913 Solving -3.125 + x = -2.831187913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = -2.831187913 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -2.831187913 + 3.125 x = -2.831187913 + 3.125 Combine like terms: -2.831187913 + 3.125 = 0.293812087 x = 0.293812087 Simplifying x = 0.293812087Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.956187913, 0.293812087}
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