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Simplifying (2x + 5)(6x + -1) = 210 Reorder the terms: (5 + 2x)(6x + -1) = 210 Reorder the terms: (5 + 2x)(-1 + 6x) = 210 Multiply (5 + 2x) * (-1 + 6x) (5(-1 + 6x) + 2x * (-1 + 6x)) = 210 ((-1 * 5 + 6x * 5) + 2x * (-1 + 6x)) = 210 ((-5 + 30x) + 2x * (-1 + 6x)) = 210 (-5 + 30x + (-1 * 2x + 6x * 2x)) = 210 (-5 + 30x + (-2x + 12x2)) = 210 Combine like terms: 30x + -2x = 28x (-5 + 28x + 12x2) = 210 Solving -5 + 28x + 12x2 = 210 Solving for variable 'x'. Reorder the terms: -5 + -210 + 28x + 12x2 = 210 + -210 Combine like terms: -5 + -210 = -215 -215 + 28x + 12x2 = 210 + -210 Combine like terms: 210 + -210 = 0 -215 + 28x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -17.91666667 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '17.91666667' to each side of the equation. -17.91666667 + 2.333333333x + 17.91666667 + x2 = 0 + 17.91666667 Reorder the terms: -17.91666667 + 17.91666667 + 2.333333333x + x2 = 0 + 17.91666667 Combine like terms: -17.91666667 + 17.91666667 = 0.00000000 0.00000000 + 2.333333333x + x2 = 0 + 17.91666667 2.333333333x + x2 = 0 + 17.91666667 Combine like terms: 0 + 17.91666667 = 17.91666667 2.333333333x + x2 = 17.91666667 The x term is 2.333333333x. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333x + 1.361111112 + x2 = 17.91666667 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = 17.91666667 + 1.361111112 Combine like terms: 17.91666667 + 1.361111112 = 19.277777782 1.361111112 + 2.333333333x + x2 = 19.277777782 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 19.277777782 Calculate the square root of the right side: 4.390646625 Break this problem into two subproblems by setting (x + 1.166666667) equal to 4.390646625 and -4.390646625.Subproblem 1
x + 1.166666667 = 4.390646625 Simplifying x + 1.166666667 = 4.390646625 Reorder the terms: 1.166666667 + x = 4.390646625 Solving 1.166666667 + x = 4.390646625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 4.390646625 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 4.390646625 + -1.166666667 x = 4.390646625 + -1.166666667 Combine like terms: 4.390646625 + -1.166666667 = 3.223979958 x = 3.223979958 Simplifying x = 3.223979958Subproblem 2
x + 1.166666667 = -4.390646625 Simplifying x + 1.166666667 = -4.390646625 Reorder the terms: 1.166666667 + x = -4.390646625 Solving 1.166666667 + x = -4.390646625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -4.390646625 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -4.390646625 + -1.166666667 x = -4.390646625 + -1.166666667 Combine like terms: -4.390646625 + -1.166666667 = -5.557313292 x = -5.557313292 Simplifying x = -5.557313292Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.223979958, -5.557313292}
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