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Simplifying 5x(x + 3) + 4 = 9 + -1(x + 1) Reorder the terms: 5x(3 + x) + 4 = 9 + -1(x + 1) (3 * 5x + x * 5x) + 4 = 9 + -1(x + 1) (15x + 5x2) + 4 = 9 + -1(x + 1) Reorder the terms: 4 + 15x + 5x2 = 9 + -1(x + 1) Reorder the terms: 4 + 15x + 5x2 = 9 + -1(1 + x) 4 + 15x + 5x2 = 9 + (1 * -1 + x * -1) 4 + 15x + 5x2 = 9 + (-1 + -1x) Combine like terms: 9 + -1 = 8 4 + 15x + 5x2 = 8 + -1x Solving 4 + 15x + 5x2 = 8 + -1x Solving for variable 'x'. Reorder the terms: 4 + -8 + 15x + x + 5x2 = 8 + -1x + -8 + x Combine like terms: 4 + -8 = -4 -4 + 15x + x + 5x2 = 8 + -1x + -8 + x Combine like terms: 15x + x = 16x -4 + 16x + 5x2 = 8 + -1x + -8 + x Reorder the terms: -4 + 16x + 5x2 = 8 + -8 + -1x + x Combine like terms: 8 + -8 = 0 -4 + 16x + 5x2 = 0 + -1x + x -4 + 16x + 5x2 = -1x + x Combine like terms: -1x + x = 0 -4 + 16x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + 3.2x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 3.2x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 3.2x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 3.2x + x2 = 0 + 0.8 3.2x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 3.2x + x2 = 0.8 The x term is 3.2x. Take half its coefficient (1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. 3.2x + 2.56 + x2 = 0.8 + 2.56 Reorder the terms: 2.56 + 3.2x + x2 = 0.8 + 2.56 Combine like terms: 0.8 + 2.56 = 3.36 2.56 + 3.2x + x2 = 3.36 Factor a perfect square on the left side: (x + 1.6)(x + 1.6) = 3.36 Calculate the square root of the right side: 1.833030278 Break this problem into two subproblems by setting (x + 1.6) equal to 1.833030278 and -1.833030278.Subproblem 1
x + 1.6 = 1.833030278 Simplifying x + 1.6 = 1.833030278 Reorder the terms: 1.6 + x = 1.833030278 Solving 1.6 + x = 1.833030278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = 1.833030278 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = 1.833030278 + -1.6 x = 1.833030278 + -1.6 Combine like terms: 1.833030278 + -1.6 = 0.233030278 x = 0.233030278 Simplifying x = 0.233030278Subproblem 2
x + 1.6 = -1.833030278 Simplifying x + 1.6 = -1.833030278 Reorder the terms: 1.6 + x = -1.833030278 Solving 1.6 + x = -1.833030278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = -1.833030278 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = -1.833030278 + -1.6 x = -1.833030278 + -1.6 Combine like terms: -1.833030278 + -1.6 = -3.433030278 x = -3.433030278 Simplifying x = -3.433030278Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.233030278, -3.433030278}
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