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Simplifying -2x2 + 12x + 17 = 0 Reorder the terms: 17 + 12x + -2x2 = 0 Solving 17 + 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'. -8.5 + -6x + x2 = 0 Move the constant term to the right: Add '8.5' to each side of the equation. -8.5 + -6x + 8.5 + x2 = 0 + 8.5 Reorder the terms: -8.5 + 8.5 + -6x + x2 = 0 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + -6x + x2 = 0 + 8.5 -6x + x2 = 0 + 8.5 Combine like terms: 0 + 8.5 = 8.5 -6x + x2 = 8.5 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 = 8.5 + 9 Reorder the terms: 9 + -6x + x2 = 8.5 + 9 Combine like terms: 8.5 + 9 = 17.5 9 + -6x + x2 = 17.5 Factor a perfect square on the left side: (x + -3)(x + -3) = 17.5 Calculate the square root of the right side: 4.183300133 Break this problem into two subproblems by setting (x + -3) equal to 4.183300133 and -4.183300133.Subproblem 1
x + -3 = 4.183300133 Simplifying x + -3 = 4.183300133 Reorder the terms: -3 + x = 4.183300133 Solving -3 + x = 4.183300133 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 = 4.183300133 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.183300133 + 3 x = 4.183300133 + 3 Combine like terms: 4.183300133 + 3 = 7.183300133 x = 7.183300133 Simplifying x = 7.183300133Subproblem 2
x + -3 = -4.183300133 Simplifying x + -3 = -4.183300133 Reorder the terms: -3 + x = -4.183300133 Solving -3 + x = -4.183300133 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 = -4.183300133 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.183300133 + 3 x = -4.183300133 + 3 Combine like terms: -4.183300133 + 3 = -1.183300133 x = -1.183300133 Simplifying x = -1.183300133Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.183300133, -1.183300133}
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