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Simplifying -4x2 + 1x = -17 Reorder the terms: 1x + -4x2 = -17 Solving 1x + -4x2 = -17 Solving for variable 'x'. Reorder the terms: 17 + 1x + -4x2 = -17 + 17 Combine like terms: -17 + 17 = 0 17 + 1x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -4.25 + -0.25x + x2 = 0 Move the constant term to the right: Add '4.25' to each side of the equation. -4.25 + -0.25x + 4.25 + x2 = 0 + 4.25 Reorder the terms: -4.25 + 4.25 + -0.25x + x2 = 0 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + -0.25x + x2 = 0 + 4.25 -0.25x + x2 = 0 + 4.25 Combine like terms: 0 + 4.25 = 4.25 -0.25x + x2 = 4.25 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 4.25 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 4.25 + 0.015625 Combine like terms: 4.25 + 0.015625 = 4.265625 0.015625 + -0.25x + x2 = 4.265625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 4.265625 Calculate the square root of the right side: 2.065338955 Break this problem into two subproblems by setting (x + -0.125) equal to 2.065338955 and -2.065338955.Subproblem 1
x + -0.125 = 2.065338955 Simplifying x + -0.125 = 2.065338955 Reorder the terms: -0.125 + x = 2.065338955 Solving -0.125 + x = 2.065338955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 2.065338955 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 2.065338955 + 0.125 x = 2.065338955 + 0.125 Combine like terms: 2.065338955 + 0.125 = 2.190338955 x = 2.190338955 Simplifying x = 2.190338955Subproblem 2
x + -0.125 = -2.065338955 Simplifying x + -0.125 = -2.065338955 Reorder the terms: -0.125 + x = -2.065338955 Solving -0.125 + x = -2.065338955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -2.065338955 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -2.065338955 + 0.125 x = -2.065338955 + 0.125 Combine like terms: -2.065338955 + 0.125 = -1.940338955 x = -1.940338955 Simplifying x = -1.940338955Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.190338955, -1.940338955}
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