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Simplifying 6x2 + 12 = 5x + 3 Reorder the terms: 12 + 6x2 = 5x + 3 Reorder the terms: 12 + 6x2 = 3 + 5x Solving 12 + 6x2 = 3 + 5x Solving for variable 'x'. Reorder the terms: 12 + -3 + -5x + 6x2 = 3 + 5x + -3 + -5x Combine like terms: 12 + -3 = 9 9 + -5x + 6x2 = 3 + 5x + -3 + -5x Reorder the terms: 9 + -5x + 6x2 = 3 + -3 + 5x + -5x Combine like terms: 3 + -3 = 0 9 + -5x + 6x2 = 0 + 5x + -5x 9 + -5x + 6x2 = 5x + -5x Combine like terms: 5x + -5x = 0 9 + -5x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.5 + -0.8333333333x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -0.8333333333x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -0.8333333333x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -0.8333333333x + x2 = 0 + -1.5 -0.8333333333x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -0.8333333333x + x2 = -1.5 The x term is -0.8333333333x. Take half its coefficient (-0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. -0.8333333333x + 0.1736111111 + x2 = -1.5 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333x + x2 = -1.5 + 0.1736111111 Combine like terms: -1.5 + 0.1736111111 = -1.3263888889 0.1736111111 + -0.8333333333x + x2 = -1.3263888889 Factor a perfect square on the left side: (x + -0.4166666667)(x + -0.4166666667) = -1.3263888889 Can't calculate square root of the right side. The solution to this equation could not be determined.
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