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Simplifying (5x + 3)(x + (-2)) = 8 Reorder the terms: (3 + 5x)(x + (-2)) = 8 (3 + 5x)(x + -2) = 8 Reorder the terms: (3 + 5x)(-2 + x) = 8 Multiply (3 + 5x) * (-2 + x) (3(-2 + x) + 5x * (-2 + x)) = 8 ((-2 * 3 + x * 3) + 5x * (-2 + x)) = 8 ((-6 + 3x) + 5x * (-2 + x)) = 8 (-6 + 3x + (-2 * 5x + x * 5x)) = 8 (-6 + 3x + (-10x + 5x2)) = 8 Combine like terms: 3x + -10x = -7x (-6 + -7x + 5x2) = 8 Solving -6 + -7x + 5x2 = 8 Solving for variable 'x'. Reorder the terms: -6 + -8 + -7x + 5x2 = 8 + -8 Combine like terms: -6 + -8 = -14 -14 + -7x + 5x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -14 + -7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.8 + -1.4x + x2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + -1.4x + 2.8 + x2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + -1.4x + x2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + -1.4x + x2 = 0 + 2.8 -1.4x + x2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 -1.4x + x2 = 2.8 The x term is -1.4x. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x + 0.49 + x2 = 2.8 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = 2.8 + 0.49 Combine like terms: 2.8 + 0.49 = 3.29 0.49 + -1.4x + x2 = 3.29 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 3.29 Calculate the square root of the right side: 1.813835715 Break this problem into two subproblems by setting (x + -0.7) equal to 1.813835715 and -1.813835715.Subproblem 1
x + -0.7 = 1.813835715 Simplifying x + -0.7 = 1.813835715 Reorder the terms: -0.7 + x = 1.813835715 Solving -0.7 + x = 1.813835715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 1.813835715 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 1.813835715 + 0.7 x = 1.813835715 + 0.7 Combine like terms: 1.813835715 + 0.7 = 2.513835715 x = 2.513835715 Simplifying x = 2.513835715Subproblem 2
x + -0.7 = -1.813835715 Simplifying x + -0.7 = -1.813835715 Reorder the terms: -0.7 + x = -1.813835715 Solving -0.7 + x = -1.813835715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = -1.813835715 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -1.813835715 + 0.7 x = -1.813835715 + 0.7 Combine like terms: -1.813835715 + 0.7 = -1.113835715 x = -1.113835715 Simplifying x = -1.113835715Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.513835715, -1.113835715}
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