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Simplifying 2x2 + 12x + -23 = 0 Reorder the terms: -23 + 12x + 2x2 = 0 Solving -23 + 12x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -11.5 + 6x + x2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + 6x + 11.5 + x2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + 6x + x2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + 6x + x2 = 0 + 11.5 6x + x2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 6x + x2 = 11.5 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 = 11.5 + 9 Reorder the terms: 9 + 6x + x2 = 11.5 + 9 Combine like terms: 11.5 + 9 = 20.5 9 + 6x + x2 = 20.5 Factor a perfect square on the left side: (x + 3)(x + 3) = 20.5 Calculate the square root of the right side: 4.527692569 Break this problem into two subproblems by setting (x + 3) equal to 4.527692569 and -4.527692569.Subproblem 1
x + 3 = 4.527692569 Simplifying x + 3 = 4.527692569 Reorder the terms: 3 + x = 4.527692569 Solving 3 + x = 4.527692569 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 = 4.527692569 + -3 Combine like terms: 3 + -3 = 0 0 + x = 4.527692569 + -3 x = 4.527692569 + -3 Combine like terms: 4.527692569 + -3 = 1.527692569 x = 1.527692569 Simplifying x = 1.527692569Subproblem 2
x + 3 = -4.527692569 Simplifying x + 3 = -4.527692569 Reorder the terms: 3 + x = -4.527692569 Solving 3 + x = -4.527692569 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 = -4.527692569 + -3 Combine like terms: 3 + -3 = 0 0 + x = -4.527692569 + -3 x = -4.527692569 + -3 Combine like terms: -4.527692569 + -3 = -7.527692569 x = -7.527692569 Simplifying x = -7.527692569Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.527692569, -7.527692569}
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