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Simplifying 4x2 + 17x = 5 Reorder the terms: 17x + 4x2 = 5 Solving 17x + 4x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 17x + 4x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 17x + 4x2 = 0 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 = 0.276171589 x = 0.276171589 Simplifying x = 0.276171589Subproblem 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 = -4.526171589 x = -4.526171589 Simplifying x = -4.526171589Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.276171589, -4.526171589}
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