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Simplifying x2 + -1x + -2 = x2 + -66x + x2 + 64 Reorder the terms: -2 + -1x + x2 = x2 + -66x + x2 + 64 Reorder the terms: -2 + -1x + x2 = 64 + -66x + x2 + x2 Combine like terms: x2 + x2 = 2x2 -2 + -1x + x2 = 64 + -66x + 2x2 Solving -2 + -1x + x2 = 64 + -66x + 2x2 Solving for variable 'x'. Reorder the terms: -2 + -64 + -1x + 66x + x2 + -2x2 = 64 + -66x + 2x2 + -64 + 66x + -2x2 Combine like terms: -2 + -64 = -66 -66 + -1x + 66x + x2 + -2x2 = 64 + -66x + 2x2 + -64 + 66x + -2x2 Combine like terms: -1x + 66x = 65x -66 + 65x + x2 + -2x2 = 64 + -66x + 2x2 + -64 + 66x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -66 + 65x + -1x2 = 64 + -66x + 2x2 + -64 + 66x + -2x2 Reorder the terms: -66 + 65x + -1x2 = 64 + -64 + -66x + 66x + 2x2 + -2x2 Combine like terms: 64 + -64 = 0 -66 + 65x + -1x2 = 0 + -66x + 66x + 2x2 + -2x2 -66 + 65x + -1x2 = -66x + 66x + 2x2 + -2x2 Combine like terms: -66x + 66x = 0 -66 + 65x + -1x2 = 0 + 2x2 + -2x2 -66 + 65x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -66 + 65x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 66 + -65x + x2 = 0 Move the constant term to the right: Add '-66' to each side of the equation. 66 + -65x + -66 + x2 = 0 + -66 Reorder the terms: 66 + -66 + -65x + x2 = 0 + -66 Combine like terms: 66 + -66 = 0 0 + -65x + x2 = 0 + -66 -65x + x2 = 0 + -66 Combine like terms: 0 + -66 = -66 -65x + x2 = -66 The x term is -65x. Take half its coefficient (-32.5). Square it (1056.25) and add it to both sides. Add '1056.25' to each side of the equation. -65x + 1056.25 + x2 = -66 + 1056.25 Reorder the terms: 1056.25 + -65x + x2 = -66 + 1056.25 Combine like terms: -66 + 1056.25 = 990.25 1056.25 + -65x + x2 = 990.25 Factor a perfect square on the left side: (x + -32.5)(x + -32.5) = 990.25 Calculate the square root of the right side: 31.468237955 Break this problem into two subproblems by setting (x + -32.5) equal to 31.468237955 and -31.468237955.Subproblem 1
x + -32.5 = 31.468237955 Simplifying x + -32.5 = 31.468237955 Reorder the terms: -32.5 + x = 31.468237955 Solving -32.5 + x = 31.468237955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '32.5' to each side of the equation. -32.5 + 32.5 + x = 31.468237955 + 32.5 Combine like terms: -32.5 + 32.5 = 0.0 0.0 + x = 31.468237955 + 32.5 x = 31.468237955 + 32.5 Combine like terms: 31.468237955 + 32.5 = 63.968237955 x = 63.968237955 Simplifying x = 63.968237955Subproblem 2
x + -32.5 = -31.468237955 Simplifying x + -32.5 = -31.468237955 Reorder the terms: -32.5 + x = -31.468237955 Solving -32.5 + x = -31.468237955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '32.5' to each side of the equation. -32.5 + 32.5 + x = -31.468237955 + 32.5 Combine like terms: -32.5 + 32.5 = 0.0 0.0 + x = -31.468237955 + 32.5 x = -31.468237955 + 32.5 Combine like terms: -31.468237955 + 32.5 = 1.031762045 x = 1.031762045 Simplifying x = 1.031762045Solution
The solution to the problem is based on the solutions from the subproblems. x = {63.968237955, 1.031762045}
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