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Simplifying 5x2 + -2x + 7 = x2 + 6x Reorder the terms: 7 + -2x + 5x2 = x2 + 6x Reorder the terms: 7 + -2x + 5x2 = 6x + x2 Solving 7 + -2x + 5x2 = 6x + x2 Solving for variable 'x'. Reorder the terms: 7 + -2x + -6x + 5x2 + -1x2 = 6x + x2 + -6x + -1x2 Combine like terms: -2x + -6x = -8x 7 + -8x + 5x2 + -1x2 = 6x + x2 + -6x + -1x2 Combine like terms: 5x2 + -1x2 = 4x2 7 + -8x + 4x2 = 6x + x2 + -6x + -1x2 Reorder the terms: 7 + -8x + 4x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 7 + -8x + 4x2 = 0 + x2 + -1x2 7 + -8x + 4x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 7 + -8x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + -2x + x2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + -2x + -1.75 + x2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + -2x + x2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + -2x + x2 = 0 + -1.75 -2x + x2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 -2x + x2 = -1.75 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -1.75 + 1 Reorder the terms: 1 + -2x + x2 = -1.75 + 1 Combine like terms: -1.75 + 1 = -0.75 1 + -2x + x2 = -0.75 Factor a perfect square on the left side: (x + -1)(x + -1) = -0.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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