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Simplifying 3x(x + -4) + 8 = 2(x2 + -6) + 57 Reorder the terms: 3x(-4 + x) + 8 = 2(x2 + -6) + 57 (-4 * 3x + x * 3x) + 8 = 2(x2 + -6) + 57 (-12x + 3x2) + 8 = 2(x2 + -6) + 57 Reorder the terms: 8 + -12x + 3x2 = 2(x2 + -6) + 57 Reorder the terms: 8 + -12x + 3x2 = 2(-6 + x2) + 57 8 + -12x + 3x2 = (-6 * 2 + x2 * 2) + 57 8 + -12x + 3x2 = (-12 + 2x2) + 57 Reorder the terms: 8 + -12x + 3x2 = -12 + 57 + 2x2 Combine like terms: -12 + 57 = 45 8 + -12x + 3x2 = 45 + 2x2 Solving 8 + -12x + 3x2 = 45 + 2x2 Solving for variable 'x'. Reorder the terms: 8 + -45 + -12x + 3x2 + -2x2 = 45 + 2x2 + -45 + -2x2 Combine like terms: 8 + -45 = -37 -37 + -12x + 3x2 + -2x2 = 45 + 2x2 + -45 + -2x2 Combine like terms: 3x2 + -2x2 = 1x2 -37 + -12x + 1x2 = 45 + 2x2 + -45 + -2x2 Reorder the terms: -37 + -12x + 1x2 = 45 + -45 + 2x2 + -2x2 Combine like terms: 45 + -45 = 0 -37 + -12x + 1x2 = 0 + 2x2 + -2x2 -37 + -12x + 1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -37 + -12x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + -12x + 37 + x2 = 0 + 37 Reorder the terms: -37 + 37 + -12x + x2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + -12x + x2 = 0 + 37 -12x + x2 = 0 + 37 Combine like terms: 0 + 37 = 37 -12x + x2 = 37 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 37 + 36 Reorder the terms: 36 + -12x + x2 = 37 + 36 Combine like terms: 37 + 36 = 73 36 + -12x + x2 = 73 Factor a perfect square on the left side: (x + -6)(x + -6) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (x + -6) equal to 8.544003745 and -8.544003745.Subproblem 1
x + -6 = 8.544003745 Simplifying x + -6 = 8.544003745 Reorder the terms: -6 + x = 8.544003745 Solving -6 + x = 8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 8.544003745 + 6 Combine like terms: -6 + 6 = 0 0 + x = 8.544003745 + 6 x = 8.544003745 + 6 Combine like terms: 8.544003745 + 6 = 14.544003745 x = 14.544003745 Simplifying x = 14.544003745Subproblem 2
x + -6 = -8.544003745 Simplifying x + -6 = -8.544003745 Reorder the terms: -6 + x = -8.544003745 Solving -6 + x = -8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -8.544003745 + 6 Combine like terms: -6 + 6 = 0 0 + x = -8.544003745 + 6 x = -8.544003745 + 6 Combine like terms: -8.544003745 + 6 = -2.544003745 x = -2.544003745 Simplifying x = -2.544003745Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.544003745, -2.544003745}
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