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Simplifying (3x + 7)(2x + -7) + 90 = 180 Reorder the terms: (7 + 3x)(2x + -7) + 90 = 180 Reorder the terms: (7 + 3x)(-7 + 2x) + 90 = 180 Multiply (7 + 3x) * (-7 + 2x) (7(-7 + 2x) + 3x * (-7 + 2x)) + 90 = 180 ((-7 * 7 + 2x * 7) + 3x * (-7 + 2x)) + 90 = 180 ((-49 + 14x) + 3x * (-7 + 2x)) + 90 = 180 (-49 + 14x + (-7 * 3x + 2x * 3x)) + 90 = 180 (-49 + 14x + (-21x + 6x2)) + 90 = 180 Combine like terms: 14x + -21x = -7x (-49 + -7x + 6x2) + 90 = 180 Reorder the terms: -49 + 90 + -7x + 6x2 = 180 Combine like terms: -49 + 90 = 41 41 + -7x + 6x2 = 180 Solving 41 + -7x + 6x2 = 180 Solving for variable 'x'. Reorder the terms: 41 + -180 + -7x + 6x2 = 180 + -180 Combine like terms: 41 + -180 = -139 -139 + -7x + 6x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -139 + -7x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -23.16666667 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '23.16666667' to each side of the equation. -23.16666667 + -1.166666667x + 23.16666667 + x2 = 0 + 23.16666667 Reorder the terms: -23.16666667 + 23.16666667 + -1.166666667x + x2 = 0 + 23.16666667 Combine like terms: -23.16666667 + 23.16666667 = 0.00000000 0.00000000 + -1.166666667x + x2 = 0 + 23.16666667 -1.166666667x + x2 = 0 + 23.16666667 Combine like terms: 0 + 23.16666667 = 23.16666667 -1.166666667x + x2 = 23.16666667 The x term is -1.166666667x. Take half its coefficient (-0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. -1.166666667x + 0.3402777780 + x2 = 23.16666667 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 23.16666667 + 0.3402777780 Combine like terms: 23.16666667 + 0.3402777780 = 23.506944448 0.3402777780 + -1.166666667x + x2 = 23.506944448 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 23.506944448 Calculate the square root of the right side: 4.84839607 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 4.84839607 and -4.84839607.Subproblem 1
x + -0.5833333335 = 4.84839607 Simplifying x + -0.5833333335 = 4.84839607 Reorder the terms: -0.5833333335 + x = 4.84839607 Solving -0.5833333335 + x = 4.84839607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = 4.84839607 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 4.84839607 + 0.5833333335 x = 4.84839607 + 0.5833333335 Combine like terms: 4.84839607 + 0.5833333335 = 5.4317294035 x = 5.4317294035 Simplifying x = 5.4317294035Subproblem 2
x + -0.5833333335 = -4.84839607 Simplifying x + -0.5833333335 = -4.84839607 Reorder the terms: -0.5833333335 + x = -4.84839607 Solving -0.5833333335 + x = -4.84839607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = -4.84839607 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -4.84839607 + 0.5833333335 x = -4.84839607 + 0.5833333335 Combine like terms: -4.84839607 + 0.5833333335 = -4.2650627365 x = -4.2650627365 Simplifying x = -4.2650627365Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.4317294035, -4.2650627365}
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