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Simplifying 2x2 + 12x = 5 Reorder the terms: 12x + 2x2 = 5 Solving 12x + 2x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 12x + 2x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + 6x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 6x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 6x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 6x + x2 = 0 + 2.5 6x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 6x + x2 = 2.5 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 2.5 + 9 Reorder the terms: 9 + 6x + x2 = 2.5 + 9 Combine like terms: 2.5 + 9 = 11.5 9 + 6x + x2 = 11.5 Factor a perfect square on the left side: (x + 3)(x + 3) = 11.5 Calculate the square root of the right side: 3.391164992 Break this problem into two subproblems by setting (x + 3) equal to 3.391164992 and -3.391164992.Subproblem 1
x + 3 = 3.391164992 Simplifying x + 3 = 3.391164992 Reorder the terms: 3 + x = 3.391164992 Solving 3 + x = 3.391164992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.391164992 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.391164992 + -3 x = 3.391164992 + -3 Combine like terms: 3.391164992 + -3 = 0.391164992 x = 0.391164992 Simplifying x = 0.391164992Subproblem 2
x + 3 = -3.391164992 Simplifying x + 3 = -3.391164992 Reorder the terms: 3 + x = -3.391164992 Solving 3 + x = -3.391164992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.391164992 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.391164992 + -3 x = -3.391164992 + -3 Combine like terms: -3.391164992 + -3 = -6.391164992 x = -6.391164992 Simplifying x = -6.391164992Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.391164992, -6.391164992}
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