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Simplifying x = 4x2 + 53 Reorder the terms: x = 53 + 4x2 Solving x = 53 + 4x2 Solving for variable 'x'. Reorder the terms: -53 + x + -4x2 = 53 + 4x2 + -53 + -4x2 Reorder the terms: -53 + x + -4x2 = 53 + -53 + 4x2 + -4x2 Combine like terms: 53 + -53 = 0 -53 + x + -4x2 = 0 + 4x2 + -4x2 -53 + x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -53 + x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 13.25 + -0.25x + x2 = 0 Move the constant term to the right: Add '-13.25' to each side of the equation. 13.25 + -0.25x + -13.25 + x2 = 0 + -13.25 Reorder the terms: 13.25 + -13.25 + -0.25x + x2 = 0 + -13.25 Combine like terms: 13.25 + -13.25 = 0.00 0.00 + -0.25x + x2 = 0 + -13.25 -0.25x + x2 = 0 + -13.25 Combine like terms: 0 + -13.25 = -13.25 -0.25x + x2 = -13.25 The x term is x. 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. -0.25x + 0.25 + x2 = -13.25 + 0.25 Reorder the terms: 0.25 + -0.25x + x2 = -13.25 + 0.25 Combine like terms: -13.25 + 0.25 = -13 0.25 + -0.25x + x2 = -13 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -13 Can't calculate square root of the right side. The solution to this equation could not be determined.
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