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Simplifying (2x + -5)(x + 3) = 20 Reorder the terms: (-5 + 2x)(x + 3) = 20 Reorder the terms: (-5 + 2x)(3 + x) = 20 Multiply (-5 + 2x) * (3 + x) (-5(3 + x) + 2x * (3 + x)) = 20 ((3 * -5 + x * -5) + 2x * (3 + x)) = 20 ((-15 + -5x) + 2x * (3 + x)) = 20 (-15 + -5x + (3 * 2x + x * 2x)) = 20 (-15 + -5x + (6x + 2x2)) = 20 Combine like terms: -5x + 6x = 1x (-15 + 1x + 2x2) = 20 Solving -15 + 1x + 2x2 = 20 Solving for variable 'x'. Reorder the terms: -15 + -20 + 1x + 2x2 = 20 + -20 Combine like terms: -15 + -20 = -35 -35 + 1x + 2x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -35 + 1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -17.5 + 0.5x + x2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + 0.5x + 17.5 + x2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + 0.5x + x2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + 0.5x + x2 = 0 + 17.5 0.5x + x2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 0.5x + x2 = 17.5 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 = 17.5 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 17.5 + 0.0625 Combine like terms: 17.5 + 0.0625 = 17.5625 0.0625 + 0.5x + x2 = 17.5625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 17.5625 Calculate the square root of the right side: 4.190763654 Break this problem into two subproblems by setting (x + 0.25) equal to 4.190763654 and -4.190763654.Subproblem 1
x + 0.25 = 4.190763654 Simplifying x + 0.25 = 4.190763654 Reorder the terms: 0.25 + x = 4.190763654 Solving 0.25 + x = 4.190763654 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 = 4.190763654 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 4.190763654 + -0.25 x = 4.190763654 + -0.25 Combine like terms: 4.190763654 + -0.25 = 3.940763654 x = 3.940763654 Simplifying x = 3.940763654Subproblem 2
x + 0.25 = -4.190763654 Simplifying x + 0.25 = -4.190763654 Reorder the terms: 0.25 + x = -4.190763654 Solving 0.25 + x = -4.190763654 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 = -4.190763654 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -4.190763654 + -0.25 x = -4.190763654 + -0.25 Combine like terms: -4.190763654 + -0.25 = -4.440763654 x = -4.440763654 Simplifying x = -4.440763654Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.940763654, -4.440763654}
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