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Simplifying x2 + -12x + 28 = 3x + 64 Reorder the terms: 28 + -12x + x2 = 3x + 64 Reorder the terms: 28 + -12x + x2 = 64 + 3x Solving 28 + -12x + x2 = 64 + 3x Solving for variable 'x'. Reorder the terms: 28 + -64 + -12x + -3x + x2 = 64 + 3x + -64 + -3x Combine like terms: 28 + -64 = -36 -36 + -12x + -3x + x2 = 64 + 3x + -64 + -3x Combine like terms: -12x + -3x = -15x -36 + -15x + x2 = 64 + 3x + -64 + -3x Reorder the terms: -36 + -15x + x2 = 64 + -64 + 3x + -3x Combine like terms: 64 + -64 = 0 -36 + -15x + x2 = 0 + 3x + -3x -36 + -15x + x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -36 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -15x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -15x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -15x + x2 = 0 + 36 -15x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -15x + x2 = 36 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = 36 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 36 + 56.25 Combine like terms: 36 + 56.25 = 92.25 56.25 + -15x + x2 = 92.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 92.25 Calculate the square root of the right side: 9.604686356 Break this problem into two subproblems by setting (x + -7.5) equal to 9.604686356 and -9.604686356.Subproblem 1
x + -7.5 = 9.604686356 Simplifying x + -7.5 = 9.604686356 Reorder the terms: -7.5 + x = 9.604686356 Solving -7.5 + x = 9.604686356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 9.604686356 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 9.604686356 + 7.5 x = 9.604686356 + 7.5 Combine like terms: 9.604686356 + 7.5 = 17.104686356 x = 17.104686356 Simplifying x = 17.104686356Subproblem 2
x + -7.5 = -9.604686356 Simplifying x + -7.5 = -9.604686356 Reorder the terms: -7.5 + x = -9.604686356 Solving -7.5 + x = -9.604686356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -9.604686356 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -9.604686356 + 7.5 x = -9.604686356 + 7.5 Combine like terms: -9.604686356 + 7.5 = -2.104686356 x = -2.104686356 Simplifying x = -2.104686356Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.104686356, -2.104686356}
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