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Simplifying (3x + -30)(3x + 3) + -1(2x + -1)(2x + -1) = 0 Reorder the terms: (-30 + 3x)(3x + 3) + -1(2x + -1)(2x + -1) = 0 Reorder the terms: (-30 + 3x)(3 + 3x) + -1(2x + -1)(2x + -1) = 0 Multiply (-30 + 3x) * (3 + 3x) (-30(3 + 3x) + 3x * (3 + 3x)) + -1(2x + -1)(2x + -1) = 0 ((3 * -30 + 3x * -30) + 3x * (3 + 3x)) + -1(2x + -1)(2x + -1) = 0 ((-90 + -90x) + 3x * (3 + 3x)) + -1(2x + -1)(2x + -1) = 0 (-90 + -90x + (3 * 3x + 3x * 3x)) + -1(2x + -1)(2x + -1) = 0 (-90 + -90x + (9x + 9x2)) + -1(2x + -1)(2x + -1) = 0 Combine like terms: -90x + 9x = -81x (-90 + -81x + 9x2) + -1(2x + -1)(2x + -1) = 0 Reorder the terms: -90 + -81x + 9x2 + -1(-1 + 2x)(2x + -1) = 0 Reorder the terms: -90 + -81x + 9x2 + -1(-1 + 2x)(-1 + 2x) = 0 Multiply (-1 + 2x) * (-1 + 2x) -90 + -81x + 9x2 + -1(-1(-1 + 2x) + 2x * (-1 + 2x)) = 0 -90 + -81x + 9x2 + -1((-1 * -1 + 2x * -1) + 2x * (-1 + 2x)) = 0 -90 + -81x + 9x2 + -1((1 + -2x) + 2x * (-1 + 2x)) = 0 -90 + -81x + 9x2 + -1(1 + -2x + (-1 * 2x + 2x * 2x)) = 0 -90 + -81x + 9x2 + -1(1 + -2x + (-2x + 4x2)) = 0 Combine like terms: -2x + -2x = -4x -90 + -81x + 9x2 + -1(1 + -4x + 4x2) = 0 -90 + -81x + 9x2 + (1 * -1 + -4x * -1 + 4x2 * -1) = 0 -90 + -81x + 9x2 + (-1 + 4x + -4x2) = 0 Reorder the terms: -90 + -1 + -81x + 4x + 9x2 + -4x2 = 0 Combine like terms: -90 + -1 = -91 -91 + -81x + 4x + 9x2 + -4x2 = 0 Combine like terms: -81x + 4x = -77x -91 + -77x + 9x2 + -4x2 = 0 Combine like terms: 9x2 + -4x2 = 5x2 -91 + -77x + 5x2 = 0 Solving -91 + -77x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -18.2 + -15.4x + x2 = 0 Move the constant term to the right: Add '18.2' to each side of the equation. -18.2 + -15.4x + 18.2 + x2 = 0 + 18.2 Reorder the terms: -18.2 + 18.2 + -15.4x + x2 = 0 + 18.2 Combine like terms: -18.2 + 18.2 = 0.0 0.0 + -15.4x + x2 = 0 + 18.2 -15.4x + x2 = 0 + 18.2 Combine like terms: 0 + 18.2 = 18.2 -15.4x + x2 = 18.2 The x term is -15.4x. Take half its coefficient (-7.7). Square it (59.29) and add it to both sides. Add '59.29' to each side of the equation. -15.4x + 59.29 + x2 = 18.2 + 59.29 Reorder the terms: 59.29 + -15.4x + x2 = 18.2 + 59.29 Combine like terms: 18.2 + 59.29 = 77.49 59.29 + -15.4x + x2 = 77.49 Factor a perfect square on the left side: (x + -7.7)(x + -7.7) = 77.49 Calculate the square root of the right side: 8.802840451 Break this problem into two subproblems by setting (x + -7.7) equal to 8.802840451 and -8.802840451.Subproblem 1
x + -7.7 = 8.802840451 Simplifying x + -7.7 = 8.802840451 Reorder the terms: -7.7 + x = 8.802840451 Solving -7.7 + x = 8.802840451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.7' to each side of the equation. -7.7 + 7.7 + x = 8.802840451 + 7.7 Combine like terms: -7.7 + 7.7 = 0.0 0.0 + x = 8.802840451 + 7.7 x = 8.802840451 + 7.7 Combine like terms: 8.802840451 + 7.7 = 16.502840451 x = 16.502840451 Simplifying x = 16.502840451Subproblem 2
x + -7.7 = -8.802840451 Simplifying x + -7.7 = -8.802840451 Reorder the terms: -7.7 + x = -8.802840451 Solving -7.7 + x = -8.802840451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.7' to each side of the equation. -7.7 + 7.7 + x = -8.802840451 + 7.7 Combine like terms: -7.7 + 7.7 = 0.0 0.0 + x = -8.802840451 + 7.7 x = -8.802840451 + 7.7 Combine like terms: -8.802840451 + 7.7 = -1.102840451 x = -1.102840451 Simplifying x = -1.102840451Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.502840451, -1.102840451}
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