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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 = 99x (90 + 99x + 9x2) + -1(2x + -1)(2x + -1) = 0 Reorder the terms: 90 + 99x + 9x2 + -1(-1 + 2x)(2x + -1) = 0 Reorder the terms: 90 + 99x + 9x2 + -1(-1 + 2x)(-1 + 2x) = 0 Multiply (-1 + 2x) * (-1 + 2x) 90 + 99x + 9x2 + -1(-1(-1 + 2x) + 2x * (-1 + 2x)) = 0 90 + 99x + 9x2 + -1((-1 * -1 + 2x * -1) + 2x * (-1 + 2x)) = 0 90 + 99x + 9x2 + -1((1 + -2x) + 2x * (-1 + 2x)) = 0 90 + 99x + 9x2 + -1(1 + -2x + (-1 * 2x + 2x * 2x)) = 0 90 + 99x + 9x2 + -1(1 + -2x + (-2x + 4x2)) = 0 Combine like terms: -2x + -2x = -4x 90 + 99x + 9x2 + -1(1 + -4x + 4x2) = 0 90 + 99x + 9x2 + (1 * -1 + -4x * -1 + 4x2 * -1) = 0 90 + 99x + 9x2 + (-1 + 4x + -4x2) = 0 Reorder the terms: 90 + -1 + 99x + 4x + 9x2 + -4x2 = 0 Combine like terms: 90 + -1 = 89 89 + 99x + 4x + 9x2 + -4x2 = 0 Combine like terms: 99x + 4x = 103x 89 + 103x + 9x2 + -4x2 = 0 Combine like terms: 9x2 + -4x2 = 5x2 89 + 103x + 5x2 = 0 Solving 89 + 103x + 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'. 17.8 + 20.6x + x2 = 0 Move the constant term to the right: Add '-17.8' to each side of the equation. 17.8 + 20.6x + -17.8 + x2 = 0 + -17.8 Reorder the terms: 17.8 + -17.8 + 20.6x + x2 = 0 + -17.8 Combine like terms: 17.8 + -17.8 = 0.0 0.0 + 20.6x + x2 = 0 + -17.8 20.6x + x2 = 0 + -17.8 Combine like terms: 0 + -17.8 = -17.8 20.6x + x2 = -17.8 The x term is 20.6x. Take half its coefficient (10.3). Square it (106.09) and add it to both sides. Add '106.09' to each side of the equation. 20.6x + 106.09 + x2 = -17.8 + 106.09 Reorder the terms: 106.09 + 20.6x + x2 = -17.8 + 106.09 Combine like terms: -17.8 + 106.09 = 88.29 106.09 + 20.6x + x2 = 88.29 Factor a perfect square on the left side: (x + 10.3)(x + 10.3) = 88.29 Calculate the square root of the right side: 9.396275858 Break this problem into two subproblems by setting (x + 10.3) equal to 9.396275858 and -9.396275858.Subproblem 1
x + 10.3 = 9.396275858 Simplifying x + 10.3 = 9.396275858 Reorder the terms: 10.3 + x = 9.396275858 Solving 10.3 + x = 9.396275858 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.3' to each side of the equation. 10.3 + -10.3 + x = 9.396275858 + -10.3 Combine like terms: 10.3 + -10.3 = 0.0 0.0 + x = 9.396275858 + -10.3 x = 9.396275858 + -10.3 Combine like terms: 9.396275858 + -10.3 = -0.903724142 x = -0.903724142 Simplifying x = -0.903724142Subproblem 2
x + 10.3 = -9.396275858 Simplifying x + 10.3 = -9.396275858 Reorder the terms: 10.3 + x = -9.396275858 Solving 10.3 + x = -9.396275858 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.3' to each side of the equation. 10.3 + -10.3 + x = -9.396275858 + -10.3 Combine like terms: 10.3 + -10.3 = 0.0 0.0 + x = -9.396275858 + -10.3 x = -9.396275858 + -10.3 Combine like terms: -9.396275858 + -10.3 = -19.696275858 x = -19.696275858 Simplifying x = -19.696275858Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.903724142, -19.696275858}
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