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Simplifying 2x2 + 6x = 51 Reorder the terms: 6x + 2x2 = 51 Solving 6x + 2x2 = 51 Solving for variable 'x'. Reorder the terms: -51 + 6x + 2x2 = 51 + -51 Combine like terms: 51 + -51 = 0 -51 + 6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -25.5 + 3x + x2 = 0 Move the constant term to the right: Add '25.5' to each side of the equation. -25.5 + 3x + 25.5 + x2 = 0 + 25.5 Reorder the terms: -25.5 + 25.5 + 3x + x2 = 0 + 25.5 Combine like terms: -25.5 + 25.5 = 0.0 0.0 + 3x + x2 = 0 + 25.5 3x + x2 = 0 + 25.5 Combine like terms: 0 + 25.5 = 25.5 3x + x2 = 25.5 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 = 25.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 25.5 + 2.25 Combine like terms: 25.5 + 2.25 = 27.75 2.25 + 3x + x2 = 27.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 27.75 Calculate the square root of the right side: 5.267826876 Break this problem into two subproblems by setting (x + 1.5) equal to 5.267826876 and -5.267826876.Subproblem 1
x + 1.5 = 5.267826876 Simplifying x + 1.5 = 5.267826876 Reorder the terms: 1.5 + x = 5.267826876 Solving 1.5 + x = 5.267826876 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 = 5.267826876 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 5.267826876 + -1.5 x = 5.267826876 + -1.5 Combine like terms: 5.267826876 + -1.5 = 3.767826876 x = 3.767826876 Simplifying x = 3.767826876Subproblem 2
x + 1.5 = -5.267826876 Simplifying x + 1.5 = -5.267826876 Reorder the terms: 1.5 + x = -5.267826876 Solving 1.5 + x = -5.267826876 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 = -5.267826876 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -5.267826876 + -1.5 x = -5.267826876 + -1.5 Combine like terms: -5.267826876 + -1.5 = -6.767826876 x = -6.767826876 Simplifying x = -6.767826876Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.767826876, -6.767826876}
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