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Simplifying 4x = x2 + 3x + 7 Reorder the terms: 4x = 7 + 3x + x2 Solving 4x = 7 + 3x + x2 Solving for variable 'x'. Reorder the terms: -7 + 4x + -3x + -1x2 = 7 + 3x + x2 + -7 + -3x + -1x2 Combine like terms: 4x + -3x = 1x -7 + 1x + -1x2 = 7 + 3x + x2 + -7 + -3x + -1x2 Reorder the terms: -7 + 1x + -1x2 = 7 + -7 + 3x + -3x + x2 + -1x2 Combine like terms: 7 + -7 = 0 -7 + 1x + -1x2 = 0 + 3x + -3x + x2 + -1x2 -7 + 1x + -1x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 -7 + 1x + -1x2 = 0 + x2 + -1x2 -7 + 1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -7 + 1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 7 + -1x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -1x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -1x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x + x2 = 0 + -7 -1x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -1x + x2 = -7 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -7 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -7 + 0.25 Combine like terms: -7 + 0.25 = -6.75 0.25 + -1x + x2 = -6.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -6.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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