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Simplifying 3x(2x + 4) + -1(5x) + 9 = 5x + 8 + -1(10x) Reorder the terms: 3x(4 + 2x) + -1(5x) + 9 = 5x + 8 + -1(10x) (4 * 3x + 2x * 3x) + -1(5x) + 9 = 5x + 8 + -1(10x) (12x + 6x2) + -1(5x) + 9 = 5x + 8 + -1(10x) Remove parenthesis around (5x) 12x + 6x2 + -1 * 5x + 9 = 5x + 8 + -1(10x) Multiply -1 * 5 12x + 6x2 + -5x + 9 = 5x + 8 + -1(10x) Reorder the terms: 9 + 12x + -5x + 6x2 = 5x + 8 + -1(10x) Combine like terms: 12x + -5x = 7x 9 + 7x + 6x2 = 5x + 8 + -1(10x) Remove parenthesis around (10x) 9 + 7x + 6x2 = 5x + 8 + -1 * 10x Multiply -1 * 10 9 + 7x + 6x2 = 5x + 8 + -10x Reorder the terms: 9 + 7x + 6x2 = 8 + 5x + -10x Combine like terms: 5x + -10x = -5x 9 + 7x + 6x2 = 8 + -5x Solving 9 + 7x + 6x2 = 8 + -5x Solving for variable 'x'. Reorder the terms: 9 + -8 + 7x + 5x + 6x2 = 8 + -5x + -8 + 5x Combine like terms: 9 + -8 = 1 1 + 7x + 5x + 6x2 = 8 + -5x + -8 + 5x Combine like terms: 7x + 5x = 12x 1 + 12x + 6x2 = 8 + -5x + -8 + 5x Reorder the terms: 1 + 12x + 6x2 = 8 + -8 + -5x + 5x Combine like terms: 8 + -8 = 0 1 + 12x + 6x2 = 0 + -5x + 5x 1 + 12x + 6x2 = -5x + 5x Combine like terms: -5x + 5x = 0 1 + 12x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.1666666667 + 2x + x2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + 2x + -0.1666666667 + x2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + 2x + x2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + 2x + x2 = 0 + -0.1666666667 2x + x2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 2x + x2 = -0.1666666667 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -0.1666666667 + 1 Reorder the terms: 1 + 2x + x2 = -0.1666666667 + 1 Combine like terms: -0.1666666667 + 1 = 0.8333333333 1 + 2x + x2 = 0.8333333333 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.8333333333 Calculate the square root of the right side: 0.912870929 Break this problem into two subproblems by setting (x + 1) equal to 0.912870929 and -0.912870929.Subproblem 1
x + 1 = 0.912870929 Simplifying x + 1 = 0.912870929 Reorder the terms: 1 + x = 0.912870929 Solving 1 + x = 0.912870929 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.912870929 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.912870929 + -1 x = 0.912870929 + -1 Combine like terms: 0.912870929 + -1 = -0.087129071 x = -0.087129071 Simplifying x = -0.087129071Subproblem 2
x + 1 = -0.912870929 Simplifying x + 1 = -0.912870929 Reorder the terms: 1 + x = -0.912870929 Solving 1 + x = -0.912870929 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.912870929 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.912870929 + -1 x = -0.912870929 + -1 Combine like terms: -0.912870929 + -1 = -1.912870929 x = -1.912870929 Simplifying x = -1.912870929Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.087129071, -1.912870929}
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