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Simplifying 4x2 + -17x = 43 Reorder the terms: -17x + 4x2 = 43 Solving -17x + 4x2 = 43 Solving for variable 'x'. Reorder the terms: -43 + -17x + 4x2 = 43 + -43 Combine like terms: 43 + -43 = 0 -43 + -17x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -10.75 + -4.25x + x2 = 0 Move the constant term to the right: Add '10.75' to each side of the equation. -10.75 + -4.25x + 10.75 + x2 = 0 + 10.75 Reorder the terms: -10.75 + 10.75 + -4.25x + x2 = 0 + 10.75 Combine like terms: -10.75 + 10.75 = 0.00 0.00 + -4.25x + x2 = 0 + 10.75 -4.25x + x2 = 0 + 10.75 Combine like terms: 0 + 10.75 = 10.75 -4.25x + x2 = 10.75 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 = 10.75 + 4.515625 Reorder the terms: 4.515625 + -4.25x + x2 = 10.75 + 4.515625 Combine like terms: 10.75 + 4.515625 = 15.265625 4.515625 + -4.25x + x2 = 15.265625 Factor a perfect square on the left side: (x + -2.125)(x + -2.125) = 15.265625 Calculate the square root of the right side: 3.907124902 Break this problem into two subproblems by setting (x + -2.125) equal to 3.907124902 and -3.907124902.Subproblem 1
x + -2.125 = 3.907124902 Simplifying x + -2.125 = 3.907124902 Reorder the terms: -2.125 + x = 3.907124902 Solving -2.125 + x = 3.907124902 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 = 3.907124902 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = 3.907124902 + 2.125 x = 3.907124902 + 2.125 Combine like terms: 3.907124902 + 2.125 = 6.032124902 x = 6.032124902 Simplifying x = 6.032124902Subproblem 2
x + -2.125 = -3.907124902 Simplifying x + -2.125 = -3.907124902 Reorder the terms: -2.125 + x = -3.907124902 Solving -2.125 + x = -3.907124902 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 = -3.907124902 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = -3.907124902 + 2.125 x = -3.907124902 + 2.125 Combine like terms: -3.907124902 + 2.125 = -1.782124902 x = -1.782124902 Simplifying x = -1.782124902Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.032124902, -1.782124902}
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