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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 = 3.223110997 x = 3.223110997 Simplifying x = 3.223110997Subproblem 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 = -3.723110997 x = -3.723110997 Simplifying x = -3.723110997Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.223110997, -3.723110997}
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