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Simplifying 4x2 + 17x + -66 = 0 Reorder the terms: -66 + 17x + 4x2 = 0 Solving -66 + 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'. -16.5 + 4.25x + x2 = 0 Move the constant term to the right: Add '16.5' to each side of the equation. -16.5 + 4.25x + 16.5 + x2 = 0 + 16.5 Reorder the terms: -16.5 + 16.5 + 4.25x + x2 = 0 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + 4.25x + x2 = 0 + 16.5 4.25x + x2 = 0 + 16.5 Combine like terms: 0 + 16.5 = 16.5 4.25x + x2 = 16.5 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 = 16.5 + 4.515625 Reorder the terms: 4.515625 + 4.25x + x2 = 16.5 + 4.515625 Combine like terms: 16.5 + 4.515625 = 21.015625 4.515625 + 4.25x + x2 = 21.015625 Factor a perfect square on the left side: (x + 2.125)(x + 2.125) = 21.015625 Calculate the square root of the right side: 4.584280205 Break this problem into two subproblems by setting (x + 2.125) equal to 4.584280205 and -4.584280205.Subproblem 1
x + 2.125 = 4.584280205 Simplifying x + 2.125 = 4.584280205 Reorder the terms: 2.125 + x = 4.584280205 Solving 2.125 + x = 4.584280205 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 = 4.584280205 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = 4.584280205 + -2.125 x = 4.584280205 + -2.125 Combine like terms: 4.584280205 + -2.125 = 2.459280205 x = 2.459280205 Simplifying x = 2.459280205Subproblem 2
x + 2.125 = -4.584280205 Simplifying x + 2.125 = -4.584280205 Reorder the terms: 2.125 + x = -4.584280205 Solving 2.125 + x = -4.584280205 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 = -4.584280205 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = -4.584280205 + -2.125 x = -4.584280205 + -2.125 Combine like terms: -4.584280205 + -2.125 = -6.709280205 x = -6.709280205 Simplifying x = -6.709280205Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.459280205, -6.709280205}
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