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Simplifying (2x + 5)(x + -3) = 9 Reorder the terms: (5 + 2x)(x + -3) = 9 Reorder the terms: (5 + 2x)(-3 + x) = 9 Multiply (5 + 2x) * (-3 + x) (5(-3 + x) + 2x * (-3 + x)) = 9 ((-3 * 5 + x * 5) + 2x * (-3 + x)) = 9 ((-15 + 5x) + 2x * (-3 + x)) = 9 (-15 + 5x + (-3 * 2x + x * 2x)) = 9 (-15 + 5x + (-6x + 2x2)) = 9 Combine like terms: 5x + -6x = -1x (-15 + -1x + 2x2) = 9 Solving -15 + -1x + 2x2 = 9 Solving for variable 'x'. Reorder the terms: -15 + -9 + -1x + 2x2 = 9 + -9 Combine like terms: -15 + -9 = -24 -24 + -1x + 2x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -24 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12 + -0.5x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -0.5x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -0.5x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -0.5x + x2 = 0 + 12 -0.5x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -0.5x + x2 = 12 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 = 12 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 12 + 0.0625 Combine like terms: 12 + 0.0625 = 12.0625 0.0625 + -0.5x + x2 = 12.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 12.0625 Calculate the square root of the right side: 3.473110997 Break this problem into two subproblems by setting (x + -0.25) equal to 3.473110997 and -3.473110997.Subproblem 1
x + -0.25 = 3.473110997 Simplifying x + -0.25 = 3.473110997 Reorder the terms: -0.25 + x = 3.473110997 Solving -0.25 + x = 3.473110997 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 = 3.473110997 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 3.473110997 + 0.25 x = 3.473110997 + 0.25 Combine like terms: 3.473110997 + 0.25 = 3.723110997 x = 3.723110997 Simplifying x = 3.723110997Subproblem 2
x + -0.25 = -3.473110997 Simplifying x + -0.25 = -3.473110997 Reorder the terms: -0.25 + x = -3.473110997 Solving -0.25 + x = -3.473110997 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 = -3.473110997 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -3.473110997 + 0.25 x = -3.473110997 + 0.25 Combine like terms: -3.473110997 + 0.25 = -3.223110997 x = -3.223110997 Simplifying x = -3.223110997Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.723110997, -3.223110997}
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