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Simplifying 4x2 + -6x + -17 = 0 Reorder the terms: -17 + -6x + 4x2 = 0 Solving -17 + -6x + 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'. -4.25 + -1.5x + x2 = 0 Move the constant term to the right: Add '4.25' to each side of the equation. -4.25 + -1.5x + 4.25 + x2 = 0 + 4.25 Reorder the terms: -4.25 + 4.25 + -1.5x + x2 = 0 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + -1.5x + x2 = 0 + 4.25 -1.5x + x2 = 0 + 4.25 Combine like terms: 0 + 4.25 = 4.25 -1.5x + x2 = 4.25 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 4.25 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 4.25 + 0.5625 Combine like terms: 4.25 + 0.5625 = 4.8125 0.5625 + -1.5x + x2 = 4.8125 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 4.8125 Calculate the square root of the right side: 2.193741097 Break this problem into two subproblems by setting (x + -0.75) equal to 2.193741097 and -2.193741097.Subproblem 1
x + -0.75 = 2.193741097 Simplifying x + -0.75 = 2.193741097 Reorder the terms: -0.75 + x = 2.193741097 Solving -0.75 + x = 2.193741097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 2.193741097 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 2.193741097 + 0.75 x = 2.193741097 + 0.75 Combine like terms: 2.193741097 + 0.75 = 2.943741097 x = 2.943741097 Simplifying x = 2.943741097Subproblem 2
x + -0.75 = -2.193741097 Simplifying x + -0.75 = -2.193741097 Reorder the terms: -0.75 + x = -2.193741097 Solving -0.75 + x = -2.193741097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -2.193741097 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -2.193741097 + 0.75 x = -2.193741097 + 0.75 Combine like terms: -2.193741097 + 0.75 = -1.443741097 x = -1.443741097 Simplifying x = -1.443741097Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.943741097, -1.443741097}
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