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Simplifying x2 + -6x = 0.5x + -42 Reorder the terms: -6x + x2 = 0.5x + -42 Reorder the terms: -6x + x2 = -42 + 0.5x Solving -6x + x2 = -42 + 0.5x Solving for variable 'x'. Reorder the terms: 42 + -6x + -0.5x + x2 = -42 + 0.5x + 42 + -0.5x Combine like terms: -6x + -0.5x = -6.5x 42 + -6.5x + x2 = -42 + 0.5x + 42 + -0.5x Reorder the terms: 42 + -6.5x + x2 = -42 + 42 + 0.5x + -0.5x Combine like terms: -42 + 42 = 0 42 + -6.5x + x2 = 0 + 0.5x + -0.5x 42 + -6.5x + x2 = 0.5x + -0.5x Combine like terms: 0.5x + -0.5x = 0.0 42 + -6.5x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '-42' to each side of the equation. 42 + -6.5x + -42 + x2 = 0.0 + -42 Reorder the terms: 42 + -42 + -6.5x + x2 = 0.0 + -42 Combine like terms: 42 + -42 = 0 0 + -6.5x + x2 = 0.0 + -42 -6.5x + x2 = 0.0 + -42 Combine like terms: 0.0 + -42 = -42 -6.5x + x2 = -42 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = -42 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = -42 + 10.5625 Combine like terms: -42 + 10.5625 = -31.4375 10.5625 + -6.5x + x2 = -31.4375 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = -31.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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