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Simplifying 2x2 + 7x + 34 = x2 + -4 Reorder the terms: 34 + 7x + 2x2 = x2 + -4 Reorder the terms: 34 + 7x + 2x2 = -4 + x2 Solving 34 + 7x + 2x2 = -4 + x2 Solving for variable 'x'. Reorder the terms: 34 + 4 + 7x + 2x2 + -1x2 = -4 + x2 + 4 + -1x2 Combine like terms: 34 + 4 = 38 38 + 7x + 2x2 + -1x2 = -4 + x2 + 4 + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 38 + 7x + 1x2 = -4 + x2 + 4 + -1x2 Reorder the terms: 38 + 7x + 1x2 = -4 + 4 + x2 + -1x2 Combine like terms: -4 + 4 = 0 38 + 7x + 1x2 = 0 + x2 + -1x2 38 + 7x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 38 + 7x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-38' to each side of the equation. 38 + 7x + -38 + x2 = 0 + -38 Reorder the terms: 38 + -38 + 7x + x2 = 0 + -38 Combine like terms: 38 + -38 = 0 0 + 7x + x2 = 0 + -38 7x + x2 = 0 + -38 Combine like terms: 0 + -38 = -38 7x + x2 = -38 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -38 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -38 + 12.25 Combine like terms: -38 + 12.25 = -25.75 12.25 + 7x + x2 = -25.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = -25.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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