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Simplifying 4x2 + 17x + -6 = 0 Reorder the terms: -6 + 17x + 4x2 = 0 Solving -6 + 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'. -1.5 + 4.25x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 4.25x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 4.25x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 4.25x + x2 = 0 + 1.5 4.25x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 4.25x + x2 = 1.5 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 = 1.5 + 4.515625 Reorder the terms: 4.515625 + 4.25x + x2 = 1.5 + 4.515625 Combine like terms: 1.5 + 4.515625 = 6.015625 4.515625 + 4.25x + x2 = 6.015625 Factor a perfect square on the left side: (x + 2.125)(x + 2.125) = 6.015625 Calculate the square root of the right side: 2.452677109 Break this problem into two subproblems by setting (x + 2.125) equal to 2.452677109 and -2.452677109.Subproblem 1
x + 2.125 = 2.452677109 Simplifying x + 2.125 = 2.452677109 Reorder the terms: 2.125 + x = 2.452677109 Solving 2.125 + x = 2.452677109 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 = 2.452677109 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = 2.452677109 + -2.125 x = 2.452677109 + -2.125 Combine like terms: 2.452677109 + -2.125 = 0.327677109 x = 0.327677109 Simplifying x = 0.327677109Subproblem 2
x + 2.125 = -2.452677109 Simplifying x + 2.125 = -2.452677109 Reorder the terms: 2.125 + x = -2.452677109 Solving 2.125 + x = -2.452677109 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 = -2.452677109 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = -2.452677109 + -2.125 x = -2.452677109 + -2.125 Combine like terms: -2.452677109 + -2.125 = -4.577677109 x = -4.577677109 Simplifying x = -4.577677109Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.327677109, -4.577677109}
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