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Simplifying (2x)(x + 3) = 55 Remove parenthesis around (2x) 2x(x + 3) = 55 Reorder the terms: 2x(3 + x) = 55 (3 * 2x + x * 2x) = 55 (6x + 2x2) = 55 Solving 6x + 2x2 = 55 Solving for variable 'x'. Reorder the terms: -55 + 6x + 2x2 = 55 + -55 Combine like terms: 55 + -55 = 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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