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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 = 4.440763654 x = 4.440763654 Simplifying x = 4.440763654Subproblem 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 = -3.940763654 x = -3.940763654 Simplifying x = -3.940763654Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.440763654, -3.940763654}
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