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Simplifying 4x2 + -17x + -5 = 0 Reorder the terms: -5 + -17x + 4x2 = 0 Solving -5 + -17x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + -4.25x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -4.25x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -4.25x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -4.25x + x2 = 0 + 1.25 -4.25x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -4.25x + x2 = 1.25 The x term is -4.25x. Take half its coefficient (-2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. -4.25x + 4.515625 + x2 = 1.25 + 4.515625 Reorder the terms: 4.515625 + -4.25x + x2 = 1.25 + 4.515625 Combine like terms: 1.25 + 4.515625 = 5.765625 4.515625 + -4.25x + x2 = 5.765625 Factor a perfect square on the left side: (x + -2.125)(x + -2.125) = 5.765625 Calculate the square root of the right side: 2.401171589 Break this problem into two subproblems by setting (x + -2.125) equal to 2.401171589 and -2.401171589.Subproblem 1
x + -2.125 = 2.401171589 Simplifying x + -2.125 = 2.401171589 Reorder the terms: -2.125 + x = 2.401171589 Solving -2.125 + x = 2.401171589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = 2.401171589 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = 2.401171589 + 2.125 x = 2.401171589 + 2.125 Combine like terms: 2.401171589 + 2.125 = 4.526171589 x = 4.526171589 Simplifying x = 4.526171589Subproblem 2
x + -2.125 = -2.401171589 Simplifying x + -2.125 = -2.401171589 Reorder the terms: -2.125 + x = -2.401171589 Solving -2.125 + x = -2.401171589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = -2.401171589 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = -2.401171589 + 2.125 x = -2.401171589 + 2.125 Combine like terms: -2.401171589 + 2.125 = -0.276171589 x = -0.276171589 Simplifying x = -0.276171589Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.526171589, -0.276171589}
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