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Simplifying 2x(4x + -6) + 5 = 3x + -52 Reorder the terms: 2x(-6 + 4x) + 5 = 3x + -52 (-6 * 2x + 4x * 2x) + 5 = 3x + -52 (-12x + 8x2) + 5 = 3x + -52 Reorder the terms: 5 + -12x + 8x2 = 3x + -52 Reorder the terms: 5 + -12x + 8x2 = -52 + 3x Solving 5 + -12x + 8x2 = -52 + 3x Solving for variable 'x'. Reorder the terms: 5 + 52 + -12x + -3x + 8x2 = -52 + 3x + 52 + -3x Combine like terms: 5 + 52 = 57 57 + -12x + -3x + 8x2 = -52 + 3x + 52 + -3x Combine like terms: -12x + -3x = -15x 57 + -15x + 8x2 = -52 + 3x + 52 + -3x Reorder the terms: 57 + -15x + 8x2 = -52 + 52 + 3x + -3x Combine like terms: -52 + 52 = 0 57 + -15x + 8x2 = 0 + 3x + -3x 57 + -15x + 8x2 = 3x + -3x Combine like terms: 3x + -3x = 0 57 + -15x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 7.125 + -1.875x + x2 = 0 Move the constant term to the right: Add '-7.125' to each side of the equation. 7.125 + -1.875x + -7.125 + x2 = 0 + -7.125 Reorder the terms: 7.125 + -7.125 + -1.875x + x2 = 0 + -7.125 Combine like terms: 7.125 + -7.125 = 0.000 0.000 + -1.875x + x2 = 0 + -7.125 -1.875x + x2 = 0 + -7.125 Combine like terms: 0 + -7.125 = -7.125 -1.875x + x2 = -7.125 The x term is -1.875x. Take half its coefficient (-0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. -1.875x + 0.87890625 + x2 = -7.125 + 0.87890625 Reorder the terms: 0.87890625 + -1.875x + x2 = -7.125 + 0.87890625 Combine like terms: -7.125 + 0.87890625 = -6.24609375 0.87890625 + -1.875x + x2 = -6.24609375 Factor a perfect square on the left side: (x + -0.9375)(x + -0.9375) = -6.24609375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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