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Simplifying 7x2 + 5x = x2 + -13 Reorder the terms: 5x + 7x2 = x2 + -13 Reorder the terms: 5x + 7x2 = -13 + x2 Solving 5x + 7x2 = -13 + x2 Solving for variable 'x'. Reorder the terms: 13 + 5x + 7x2 + -1x2 = -13 + x2 + 13 + -1x2 Combine like terms: 7x2 + -1x2 = 6x2 13 + 5x + 6x2 = -13 + x2 + 13 + -1x2 Reorder the terms: 13 + 5x + 6x2 = -13 + 13 + x2 + -1x2 Combine like terms: -13 + 13 = 0 13 + 5x + 6x2 = 0 + x2 + -1x2 13 + 5x + 6x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 13 + 5x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 2.166666667 + 0.8333333333x + x2 = 0 Move the constant term to the right: Add '-2.166666667' to each side of the equation. 2.166666667 + 0.8333333333x + -2.166666667 + x2 = 0 + -2.166666667 Reorder the terms: 2.166666667 + -2.166666667 + 0.8333333333x + x2 = 0 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + 0.8333333333x + x2 = 0 + -2.166666667 0.8333333333x + x2 = 0 + -2.166666667 Combine like terms: 0 + -2.166666667 = -2.166666667 0.8333333333x + x2 = -2.166666667 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 = -2.166666667 + 0.1736111111 Reorder the terms: 0.1736111111 + 0.8333333333x + x2 = -2.166666667 + 0.1736111111 Combine like terms: -2.166666667 + 0.1736111111 = -1.9930555559 0.1736111111 + 0.8333333333x + x2 = -1.9930555559 Factor a perfect square on the left side: (x + 0.4166666667)(x + 0.4166666667) = -1.9930555559 Can't calculate square root of the right side. The solution to this equation could not be determined.
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