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Simplifying 55 = 2X(X + 3) Reorder the terms: 55 = 2X(3 + X) 55 = (3 * 2X + X * 2X) 55 = (6X + 2X2) Solving 55 = 6X + 2X2 Solving for variable 'X'. Reorder the terms: 55 + -6X + -2X2 = 6X + -6X + 2X2 + -2X2 Combine like terms: 6X + -6X = 0 55 + -6X + -2X2 = 0 + 2X2 + -2X2 55 + -6X + -2X2 = 2X2 + -2X2 Combine like terms: 2X2 + -2X2 = 0 55 + -6X + -2X2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -27.5 + 3X + X2 = 0 Move the constant term to the right: Add '27.5' to each side of the equation. -27.5 + 3X + 27.5 + X2 = 0 + 27.5 Reorder the terms: -27.5 + 27.5 + 3X + X2 = 0 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + 3X + X2 = 0 + 27.5 3X + X2 = 0 + 27.5 Combine like terms: 0 + 27.5 = 27.5 3X + X2 = 27.5 The X term is 3X. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3X + 2.25 + X2 = 27.5 + 2.25 Reorder the terms: 2.25 + 3X + X2 = 27.5 + 2.25 Combine like terms: 27.5 + 2.25 = 29.75 2.25 + 3X + X2 = 29.75 Factor a perfect square on the left side: (X + 1.5)(X + 1.5) = 29.75 Calculate the square root of the right side: 5.454356057 Break this problem into two subproblems by setting (X + 1.5) equal to 5.454356057 and -5.454356057.Subproblem 1
X + 1.5 = 5.454356057 Simplifying X + 1.5 = 5.454356057 Reorder the terms: 1.5 + X = 5.454356057 Solving 1.5 + X = 5.454356057 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + X = 5.454356057 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = 5.454356057 + -1.5 X = 5.454356057 + -1.5 Combine like terms: 5.454356057 + -1.5 = 3.954356057 X = 3.954356057 Simplifying X = 3.954356057Subproblem 2
X + 1.5 = -5.454356057 Simplifying X + 1.5 = -5.454356057 Reorder the terms: 1.5 + X = -5.454356057 Solving 1.5 + X = -5.454356057 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + X = -5.454356057 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = -5.454356057 + -1.5 X = -5.454356057 + -1.5 Combine like terms: -5.454356057 + -1.5 = -6.954356057 X = -6.954356057 Simplifying X = -6.954356057Solution
The solution to the problem is based on the solutions from the subproblems. X = {3.954356057, -6.954356057}
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