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Simplifying (6x + 7)(5x + -4) = 6(5x + -1) Reorder the terms: (7 + 6x)(5x + -4) = 6(5x + -1) Reorder the terms: (7 + 6x)(-4 + 5x) = 6(5x + -1) Multiply (7 + 6x) * (-4 + 5x) (7(-4 + 5x) + 6x * (-4 + 5x)) = 6(5x + -1) ((-4 * 7 + 5x * 7) + 6x * (-4 + 5x)) = 6(5x + -1) ((-28 + 35x) + 6x * (-4 + 5x)) = 6(5x + -1) (-28 + 35x + (-4 * 6x + 5x * 6x)) = 6(5x + -1) (-28 + 35x + (-24x + 30x2)) = 6(5x + -1) Combine like terms: 35x + -24x = 11x (-28 + 11x + 30x2) = 6(5x + -1) Reorder the terms: -28 + 11x + 30x2 = 6(-1 + 5x) -28 + 11x + 30x2 = (-1 * 6 + 5x * 6) -28 + 11x + 30x2 = (-6 + 30x) Solving -28 + 11x + 30x2 = -6 + 30x Solving for variable 'x'. Reorder the terms: -28 + 6 + 11x + -30x + 30x2 = -6 + 30x + 6 + -30x Combine like terms: -28 + 6 = -22 -22 + 11x + -30x + 30x2 = -6 + 30x + 6 + -30x Combine like terms: 11x + -30x = -19x -22 + -19x + 30x2 = -6 + 30x + 6 + -30x Reorder the terms: -22 + -19x + 30x2 = -6 + 6 + 30x + -30x Combine like terms: -6 + 6 = 0 -22 + -19x + 30x2 = 0 + 30x + -30x -22 + -19x + 30x2 = 30x + -30x Combine like terms: 30x + -30x = 0 -22 + -19x + 30x2 = 0 Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. -0.7333333333 + -0.6333333333x + x2 = 0 Move the constant term to the right: Add '0.7333333333' to each side of the equation. -0.7333333333 + -0.6333333333x + 0.7333333333 + x2 = 0 + 0.7333333333 Reorder the terms: -0.7333333333 + 0.7333333333 + -0.6333333333x + x2 = 0 + 0.7333333333 Combine like terms: -0.7333333333 + 0.7333333333 = 0.0000000000 0.0000000000 + -0.6333333333x + x2 = 0 + 0.7333333333 -0.6333333333x + x2 = 0 + 0.7333333333 Combine like terms: 0 + 0.7333333333 = 0.7333333333 -0.6333333333x + x2 = 0.7333333333 The x term is -0.6333333333x. Take half its coefficient (-0.3166666667). Square it (0.1002777778) and add it to both sides. Add '0.1002777778' to each side of the equation. -0.6333333333x + 0.1002777778 + x2 = 0.7333333333 + 0.1002777778 Reorder the terms: 0.1002777778 + -0.6333333333x + x2 = 0.7333333333 + 0.1002777778 Combine like terms: 0.7333333333 + 0.1002777778 = 0.8336111111 0.1002777778 + -0.6333333333x + x2 = 0.8336111111 Factor a perfect square on the left side: (x + -0.3166666667)(x + -0.3166666667) = 0.8336111111 Calculate the square root of the right side: 0.913023062 Break this problem into two subproblems by setting (x + -0.3166666667) equal to 0.913023062 and -0.913023062.Subproblem 1
x + -0.3166666667 = 0.913023062 Simplifying x + -0.3166666667 = 0.913023062 Reorder the terms: -0.3166666667 + x = 0.913023062 Solving -0.3166666667 + x = 0.913023062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3166666667' to each side of the equation. -0.3166666667 + 0.3166666667 + x = 0.913023062 + 0.3166666667 Combine like terms: -0.3166666667 + 0.3166666667 = 0.0000000000 0.0000000000 + x = 0.913023062 + 0.3166666667 x = 0.913023062 + 0.3166666667 Combine like terms: 0.913023062 + 0.3166666667 = 1.2296897287 x = 1.2296897287 Simplifying x = 1.2296897287Subproblem 2
x + -0.3166666667 = -0.913023062 Simplifying x + -0.3166666667 = -0.913023062 Reorder the terms: -0.3166666667 + x = -0.913023062 Solving -0.3166666667 + x = -0.913023062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3166666667' to each side of the equation. -0.3166666667 + 0.3166666667 + x = -0.913023062 + 0.3166666667 Combine like terms: -0.3166666667 + 0.3166666667 = 0.0000000000 0.0000000000 + x = -0.913023062 + 0.3166666667 x = -0.913023062 + 0.3166666667 Combine like terms: -0.913023062 + 0.3166666667 = -0.5963563953 x = -0.5963563953 Simplifying x = -0.5963563953Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2296897287, -0.5963563953}
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