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Simplifying 4X(X + 5) + -11 = 4X + 17X + 4 Reorder the terms: 4X(5 + X) + -11 = 4X + 17X + 4 (5 * 4X + X * 4X) + -11 = 4X + 17X + 4 (20X + 4X2) + -11 = 4X + 17X + 4 Reorder the terms: -11 + 20X + 4X2 = 4X + 17X + 4 Reorder the terms: -11 + 20X + 4X2 = 4 + 4X + 17X Combine like terms: 4X + 17X = 21X -11 + 20X + 4X2 = 4 + 21X Solving -11 + 20X + 4X2 = 4 + 21X Solving for variable 'X'. Reorder the terms: -11 + -4 + 20X + -21X + 4X2 = 4 + 21X + -4 + -21X Combine like terms: -11 + -4 = -15 -15 + 20X + -21X + 4X2 = 4 + 21X + -4 + -21X Combine like terms: 20X + -21X = -1X -15 + -1X + 4X2 = 4 + 21X + -4 + -21X Reorder the terms: -15 + -1X + 4X2 = 4 + -4 + 21X + -21X Combine like terms: 4 + -4 = 0 -15 + -1X + 4X2 = 0 + 21X + -21X -15 + -1X + 4X2 = 21X + -21X Combine like terms: 21X + -21X = 0 -15 + -1X + 4X2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + -0.25X + X2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -0.25X + 3.75 + X2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -0.25X + X2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -0.25X + X2 = 0 + 3.75 -0.25X + X2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -0.25X + X2 = 3.75 The X term is -0.25X. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25X + 0.015625 + X2 = 3.75 + 0.015625 Reorder the terms: 0.015625 + -0.25X + X2 = 3.75 + 0.015625 Combine like terms: 3.75 + 0.015625 = 3.765625 0.015625 + -0.25X + X2 = 3.765625 Factor a perfect square on the left side: (X + -0.125)(X + -0.125) = 3.765625 Calculate the square root of the right side: 1.940521837 Break this problem into two subproblems by setting (X + -0.125) equal to 1.940521837 and -1.940521837.Subproblem 1
X + -0.125 = 1.940521837 Simplifying X + -0.125 = 1.940521837 Reorder the terms: -0.125 + X = 1.940521837 Solving -0.125 + X = 1.940521837 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + X = 1.940521837 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + X = 1.940521837 + 0.125 X = 1.940521837 + 0.125 Combine like terms: 1.940521837 + 0.125 = 2.065521837 X = 2.065521837 Simplifying X = 2.065521837Subproblem 2
X + -0.125 = -1.940521837 Simplifying X + -0.125 = -1.940521837 Reorder the terms: -0.125 + X = -1.940521837 Solving -0.125 + X = -1.940521837 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + X = -1.940521837 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + X = -1.940521837 + 0.125 X = -1.940521837 + 0.125 Combine like terms: -1.940521837 + 0.125 = -1.815521837 X = -1.815521837 Simplifying X = -1.815521837Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.065521837, -1.815521837}
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