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Simplifying 2x2 + 6x = 111 Reorder the terms: 6x + 2x2 = 111 Solving 6x + 2x2 = 111 Solving for variable 'x'. Reorder the terms: -111 + 6x + 2x2 = 111 + -111 Combine like terms: 111 + -111 = 0 -111 + 6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -55.5 + 3x + x2 = 0 Move the constant term to the right: Add '55.5' to each side of the equation. -55.5 + 3x + 55.5 + x2 = 0 + 55.5 Reorder the terms: -55.5 + 55.5 + 3x + x2 = 0 + 55.5 Combine like terms: -55.5 + 55.5 = 0.0 0.0 + 3x + x2 = 0 + 55.5 3x + x2 = 0 + 55.5 Combine like terms: 0 + 55.5 = 55.5 3x + x2 = 55.5 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 = 55.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 55.5 + 2.25 Combine like terms: 55.5 + 2.25 = 57.75 2.25 + 3x + x2 = 57.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 57.75 Calculate the square root of the right side: 7.599342077 Break this problem into two subproblems by setting (x + 1.5) equal to 7.599342077 and -7.599342077.Subproblem 1
x + 1.5 = 7.599342077 Simplifying x + 1.5 = 7.599342077 Reorder the terms: 1.5 + x = 7.599342077 Solving 1.5 + x = 7.599342077 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 = 7.599342077 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 7.599342077 + -1.5 x = 7.599342077 + -1.5 Combine like terms: 7.599342077 + -1.5 = 6.099342077 x = 6.099342077 Simplifying x = 6.099342077Subproblem 2
x + 1.5 = -7.599342077 Simplifying x + 1.5 = -7.599342077 Reorder the terms: 1.5 + x = -7.599342077 Solving 1.5 + x = -7.599342077 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 = -7.599342077 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -7.599342077 + -1.5 x = -7.599342077 + -1.5 Combine like terms: -7.599342077 + -1.5 = -9.099342077 x = -9.099342077 Simplifying x = -9.099342077Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.099342077, -9.099342077}
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