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Simplifying 6x = 32x2 + -48x + -81 Reorder the terms: 6x = -81 + -48x + 32x2 Solving 6x = -81 + -48x + 32x2 Solving for variable 'x'. Reorder the terms: 81 + 6x + 48x + -32x2 = -81 + -48x + 32x2 + 81 + 48x + -32x2 Combine like terms: 6x + 48x = 54x 81 + 54x + -32x2 = -81 + -48x + 32x2 + 81 + 48x + -32x2 Reorder the terms: 81 + 54x + -32x2 = -81 + 81 + -48x + 48x + 32x2 + -32x2 Combine like terms: -81 + 81 = 0 81 + 54x + -32x2 = 0 + -48x + 48x + 32x2 + -32x2 81 + 54x + -32x2 = -48x + 48x + 32x2 + -32x2 Combine like terms: -48x + 48x = 0 81 + 54x + -32x2 = 0 + 32x2 + -32x2 81 + 54x + -32x2 = 32x2 + -32x2 Combine like terms: 32x2 + -32x2 = 0 81 + 54x + -32x2 = 0 Begin completing the square. Divide all terms by -32 the coefficient of the squared term: Divide each side by '-32'. -2.53125 + -1.6875x + x2 = 0 Move the constant term to the right: Add '2.53125' to each side of the equation. -2.53125 + -1.6875x + 2.53125 + x2 = 0 + 2.53125 Reorder the terms: -2.53125 + 2.53125 + -1.6875x + x2 = 0 + 2.53125 Combine like terms: -2.53125 + 2.53125 = 0.00000 0.00000 + -1.6875x + x2 = 0 + 2.53125 -1.6875x + x2 = 0 + 2.53125 Combine like terms: 0 + 2.53125 = 2.53125 -1.6875x + x2 = 2.53125 The x term is -1.6875x. Take half its coefficient (-0.84375). Square it (0.7119140625) and add it to both sides. Add '0.7119140625' to each side of the equation. -1.6875x + 0.7119140625 + x2 = 2.53125 + 0.7119140625 Reorder the terms: 0.7119140625 + -1.6875x + x2 = 2.53125 + 0.7119140625 Combine like terms: 2.53125 + 0.7119140625 = 3.2431640625 0.7119140625 + -1.6875x + x2 = 3.2431640625 Factor a perfect square on the left side: (x + -0.84375)(x + -0.84375) = 3.2431640625 Calculate the square root of the right side: 1.800878692 Break this problem into two subproblems by setting (x + -0.84375) equal to 1.800878692 and -1.800878692.Subproblem 1
x + -0.84375 = 1.800878692 Simplifying x + -0.84375 = 1.800878692 Reorder the terms: -0.84375 + x = 1.800878692 Solving -0.84375 + x = 1.800878692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.84375' to each side of the equation. -0.84375 + 0.84375 + x = 1.800878692 + 0.84375 Combine like terms: -0.84375 + 0.84375 = 0.00000 0.00000 + x = 1.800878692 + 0.84375 x = 1.800878692 + 0.84375 Combine like terms: 1.800878692 + 0.84375 = 2.644628692 x = 2.644628692 Simplifying x = 2.644628692Subproblem 2
x + -0.84375 = -1.800878692 Simplifying x + -0.84375 = -1.800878692 Reorder the terms: -0.84375 + x = -1.800878692 Solving -0.84375 + x = -1.800878692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.84375' to each side of the equation. -0.84375 + 0.84375 + x = -1.800878692 + 0.84375 Combine like terms: -0.84375 + 0.84375 = 0.00000 0.00000 + x = -1.800878692 + 0.84375 x = -1.800878692 + 0.84375 Combine like terms: -1.800878692 + 0.84375 = -0.957128692 x = -0.957128692 Simplifying x = -0.957128692Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.644628692, -0.957128692}
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