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Simplifying (2x + 5)(x + -3) = 8 Reorder the terms: (5 + 2x)(x + -3) = 8 Reorder the terms: (5 + 2x)(-3 + x) = 8 Multiply (5 + 2x) * (-3 + x) (5(-3 + x) + 2x * (-3 + x)) = 8 ((-3 * 5 + x * 5) + 2x * (-3 + x)) = 8 ((-15 + 5x) + 2x * (-3 + x)) = 8 (-15 + 5x + (-3 * 2x + x * 2x)) = 8 (-15 + 5x + (-6x + 2x2)) = 8 Combine like terms: 5x + -6x = -1x (-15 + -1x + 2x2) = 8 Solving -15 + -1x + 2x2 = 8 Solving for variable 'x'. Reorder the terms: -15 + -8 + -1x + 2x2 = 8 + -8 Combine like terms: -15 + -8 = -23 -23 + -1x + 2x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -23 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -11.5 + -0.5x + x2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + -0.5x + 11.5 + x2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + -0.5x + x2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + -0.5x + x2 = 0 + 11.5 -0.5x + x2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 -0.5x + x2 = 11.5 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 11.5 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 11.5 + 0.0625 Combine like terms: 11.5 + 0.0625 = 11.5625 0.0625 + -0.5x + x2 = 11.5625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 11.5625 Calculate the square root of the right side: 3.400367627 Break this problem into two subproblems by setting (x + -0.25) equal to 3.400367627 and -3.400367627.Subproblem 1
x + -0.25 = 3.400367627 Simplifying x + -0.25 = 3.400367627 Reorder the terms: -0.25 + x = 3.400367627 Solving -0.25 + x = 3.400367627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 3.400367627 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 3.400367627 + 0.25 x = 3.400367627 + 0.25 Combine like terms: 3.400367627 + 0.25 = 3.650367627 x = 3.650367627 Simplifying x = 3.650367627Subproblem 2
x + -0.25 = -3.400367627 Simplifying x + -0.25 = -3.400367627 Reorder the terms: -0.25 + x = -3.400367627 Solving -0.25 + x = -3.400367627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -3.400367627 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -3.400367627 + 0.25 x = -3.400367627 + 0.25 Combine like terms: -3.400367627 + 0.25 = -3.150367627 x = -3.150367627 Simplifying x = -3.150367627Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.650367627, -3.150367627}
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