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Simplifying 3x2 + -9x + -65 = x2 + -1x Reorder the terms: -65 + -9x + 3x2 = x2 + -1x Reorder the terms: -65 + -9x + 3x2 = -1x + x2 Solving -65 + -9x + 3x2 = -1x + x2 Solving for variable 'x'. Reorder the terms: -65 + -9x + x + 3x2 + -1x2 = -1x + x2 + x + -1x2 Combine like terms: -9x + x = -8x -65 + -8x + 3x2 + -1x2 = -1x + x2 + x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 -65 + -8x + 2x2 = -1x + x2 + x + -1x2 Reorder the terms: -65 + -8x + 2x2 = -1x + x + x2 + -1x2 Combine like terms: -1x + x = 0 -65 + -8x + 2x2 = 0 + x2 + -1x2 -65 + -8x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -65 + -8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -32.5 + -4x + x2 = 0 Move the constant term to the right: Add '32.5' to each side of the equation. -32.5 + -4x + 32.5 + x2 = 0 + 32.5 Reorder the terms: -32.5 + 32.5 + -4x + x2 = 0 + 32.5 Combine like terms: -32.5 + 32.5 = 0.0 0.0 + -4x + x2 = 0 + 32.5 -4x + x2 = 0 + 32.5 Combine like terms: 0 + 32.5 = 32.5 -4x + x2 = 32.5 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 32.5 + 4 Reorder the terms: 4 + -4x + x2 = 32.5 + 4 Combine like terms: 32.5 + 4 = 36.5 4 + -4x + x2 = 36.5 Factor a perfect square on the left side: (x + -2)(x + -2) = 36.5 Calculate the square root of the right side: 6.041522987 Break this problem into two subproblems by setting (x + -2) equal to 6.041522987 and -6.041522987.Subproblem 1
x + -2 = 6.041522987 Simplifying x + -2 = 6.041522987 Reorder the terms: -2 + x = 6.041522987 Solving -2 + x = 6.041522987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 6.041522987 + 2 Combine like terms: -2 + 2 = 0 0 + x = 6.041522987 + 2 x = 6.041522987 + 2 Combine like terms: 6.041522987 + 2 = 8.041522987 x = 8.041522987 Simplifying x = 8.041522987Subproblem 2
x + -2 = -6.041522987 Simplifying x + -2 = -6.041522987 Reorder the terms: -2 + x = -6.041522987 Solving -2 + x = -6.041522987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -6.041522987 + 2 Combine like terms: -2 + 2 = 0 0 + x = -6.041522987 + 2 x = -6.041522987 + 2 Combine like terms: -6.041522987 + 2 = -4.041522987 x = -4.041522987 Simplifying x = -4.041522987Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.041522987, -4.041522987}
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