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Simplifying (2x + 1)(3x + 9) = 10 Reorder the terms: (1 + 2x)(3x + 9) = 10 Reorder the terms: (1 + 2x)(9 + 3x) = 10 Multiply (1 + 2x) * (9 + 3x) (1(9 + 3x) + 2x * (9 + 3x)) = 10 ((9 * 1 + 3x * 1) + 2x * (9 + 3x)) = 10 ((9 + 3x) + 2x * (9 + 3x)) = 10 (9 + 3x + (9 * 2x + 3x * 2x)) = 10 (9 + 3x + (18x + 6x2)) = 10 Combine like terms: 3x + 18x = 21x (9 + 21x + 6x2) = 10 Solving 9 + 21x + 6x2 = 10 Solving for variable 'x'. Reorder the terms: 9 + -10 + 21x + 6x2 = 10 + -10 Combine like terms: 9 + -10 = -1 -1 + 21x + 6x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -1 + 21x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.1666666667 + 3.5x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + 3.5x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + 3.5x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + 3.5x + x2 = 0 + 0.1666666667 3.5x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 3.5x + x2 = 0.1666666667 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 0.1666666667 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 0.1666666667 + 3.0625 Combine like terms: 0.1666666667 + 3.0625 = 3.2291666667 3.0625 + 3.5x + x2 = 3.2291666667 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 3.2291666667 Calculate the square root of the right side: 1.796988221 Break this problem into two subproblems by setting (x + 1.75) equal to 1.796988221 and -1.796988221.Subproblem 1
x + 1.75 = 1.796988221 Simplifying x + 1.75 = 1.796988221 Reorder the terms: 1.75 + x = 1.796988221 Solving 1.75 + x = 1.796988221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 1.796988221 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 1.796988221 + -1.75 x = 1.796988221 + -1.75 Combine like terms: 1.796988221 + -1.75 = 0.046988221 x = 0.046988221 Simplifying x = 0.046988221Subproblem 2
x + 1.75 = -1.796988221 Simplifying x + 1.75 = -1.796988221 Reorder the terms: 1.75 + x = -1.796988221 Solving 1.75 + x = -1.796988221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -1.796988221 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -1.796988221 + -1.75 x = -1.796988221 + -1.75 Combine like terms: -1.796988221 + -1.75 = -3.546988221 x = -3.546988221 Simplifying x = -3.546988221Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.046988221, -3.546988221}
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