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Simplifying x = x2 + -14x + 65 Reorder the terms: x = 65 + -14x + x2 Solving x = 65 + -14x + x2 Solving for variable 'x'. Reorder the terms: -65 + x + 14x + -1x2 = 65 + -14x + x2 + -65 + 14x + -1x2 Combine like terms: x + 14x = 15x -65 + 15x + -1x2 = 65 + -14x + x2 + -65 + 14x + -1x2 Reorder the terms: -65 + 15x + -1x2 = 65 + -65 + -14x + 14x + x2 + -1x2 Combine like terms: 65 + -65 = 0 -65 + 15x + -1x2 = 0 + -14x + 14x + x2 + -1x2 -65 + 15x + -1x2 = -14x + 14x + x2 + -1x2 Combine like terms: -14x + 14x = 0 -65 + 15x + -1x2 = 0 + x2 + -1x2 -65 + 15x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -65 + 15x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 65 + -15x + x2 = 0 Move the constant term to the right: Add '-65' to each side of the equation. 65 + -15x + -65 + x2 = 0 + -65 Reorder the terms: 65 + -65 + -15x + x2 = 0 + -65 Combine like terms: 65 + -65 = 0 0 + -15x + x2 = 0 + -65 -15x + x2 = 0 + -65 Combine like terms: 0 + -65 = -65 -15x + x2 = -65 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -65 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -65 + 56.25 Combine like terms: -65 + 56.25 = -8.75 56.25 + -15x + x2 = -8.75 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = -8.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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