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Simplifying (2x + -5)(x + 3) = 14 Reorder the terms: (-5 + 2x)(x + 3) = 14 Reorder the terms: (-5 + 2x)(3 + x) = 14 Multiply (-5 + 2x) * (3 + x) (-5(3 + x) + 2x * (3 + x)) = 14 ((3 * -5 + x * -5) + 2x * (3 + x)) = 14 ((-15 + -5x) + 2x * (3 + x)) = 14 (-15 + -5x + (3 * 2x + x * 2x)) = 14 (-15 + -5x + (6x + 2x2)) = 14 Combine like terms: -5x + 6x = 1x (-15 + 1x + 2x2) = 14 Solving -15 + 1x + 2x2 = 14 Solving for variable 'x'. Reorder the terms: -15 + -14 + 1x + 2x2 = 14 + -14 Combine like terms: -15 + -14 = -29 -29 + 1x + 2x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -29 + 1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -14.5 + 0.5x + x2 = 0 Move the constant term to the right: Add '14.5' to each side of the equation. -14.5 + 0.5x + 14.5 + x2 = 0 + 14.5 Reorder the terms: -14.5 + 14.5 + 0.5x + x2 = 0 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + 0.5x + x2 = 0 + 14.5 0.5x + x2 = 0 + 14.5 Combine like terms: 0 + 14.5 = 14.5 0.5x + x2 = 14.5 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 = 14.5 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 14.5 + 0.0625 Combine like terms: 14.5 + 0.0625 = 14.5625 0.0625 + 0.5x + x2 = 14.5625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 14.5625 Calculate the square root of the right side: 3.816084381 Break this problem into two subproblems by setting (x + 0.25) equal to 3.816084381 and -3.816084381.Subproblem 1
x + 0.25 = 3.816084381 Simplifying x + 0.25 = 3.816084381 Reorder the terms: 0.25 + x = 3.816084381 Solving 0.25 + x = 3.816084381 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 = 3.816084381 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 3.816084381 + -0.25 x = 3.816084381 + -0.25 Combine like terms: 3.816084381 + -0.25 = 3.566084381 x = 3.566084381 Simplifying x = 3.566084381Subproblem 2
x + 0.25 = -3.816084381 Simplifying x + 0.25 = -3.816084381 Reorder the terms: 0.25 + x = -3.816084381 Solving 0.25 + x = -3.816084381 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 = -3.816084381 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -3.816084381 + -0.25 x = -3.816084381 + -0.25 Combine like terms: -3.816084381 + -0.25 = -4.066084381 x = -4.066084381 Simplifying x = -4.066084381Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.566084381, -4.066084381}
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