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Simplifying -2x2 + -12x + 37 = 0 Reorder the terms: 37 + -12x + -2x2 = 0 Solving 37 + -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'. -18.5 + 6x + x2 = 0 Move the constant term to the right: Add '18.5' to each side of the equation. -18.5 + 6x + 18.5 + x2 = 0 + 18.5 Reorder the terms: -18.5 + 18.5 + 6x + x2 = 0 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + 6x + x2 = 0 + 18.5 6x + x2 = 0 + 18.5 Combine like terms: 0 + 18.5 = 18.5 6x + x2 = 18.5 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 = 18.5 + 9 Reorder the terms: 9 + 6x + x2 = 18.5 + 9 Combine like terms: 18.5 + 9 = 27.5 9 + 6x + x2 = 27.5 Factor a perfect square on the left side: (x + 3)(x + 3) = 27.5 Calculate the square root of the right side: 5.244044241 Break this problem into two subproblems by setting (x + 3) equal to 5.244044241 and -5.244044241.Subproblem 1
x + 3 = 5.244044241 Simplifying x + 3 = 5.244044241 Reorder the terms: 3 + x = 5.244044241 Solving 3 + x = 5.244044241 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 = 5.244044241 + -3 Combine like terms: 3 + -3 = 0 0 + x = 5.244044241 + -3 x = 5.244044241 + -3 Combine like terms: 5.244044241 + -3 = 2.244044241 x = 2.244044241 Simplifying x = 2.244044241Subproblem 2
x + 3 = -5.244044241 Simplifying x + 3 = -5.244044241 Reorder the terms: 3 + x = -5.244044241 Solving 3 + x = -5.244044241 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 = -5.244044241 + -3 Combine like terms: 3 + -3 = 0 0 + x = -5.244044241 + -3 x = -5.244044241 + -3 Combine like terms: -5.244044241 + -3 = -8.244044241 x = -8.244044241 Simplifying x = -8.244044241Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.244044241, -8.244044241}
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