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Simplifying -6x2 + 12x + 17 = 7x2 Reorder the terms: 17 + 12x + -6x2 = 7x2 Solving 17 + 12x + -6x2 = 7x2 Solving for variable 'x'. Combine like terms: -6x2 + -7x2 = -13x2 17 + 12x + -13x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 17 + 12x + -13x2 = 0 Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. -1.307692308 + -0.9230769231x + x2 = 0 Move the constant term to the right: Add '1.307692308' to each side of the equation. -1.307692308 + -0.9230769231x + 1.307692308 + x2 = 0 + 1.307692308 Reorder the terms: -1.307692308 + 1.307692308 + -0.9230769231x + x2 = 0 + 1.307692308 Combine like terms: -1.307692308 + 1.307692308 = 0.000000000 0.000000000 + -0.9230769231x + x2 = 0 + 1.307692308 -0.9230769231x + x2 = 0 + 1.307692308 Combine like terms: 0 + 1.307692308 = 1.307692308 -0.9230769231x + x2 = 1.307692308 The x term is -0.9230769231x. Take half its coefficient (-0.4615384616). Square it (0.2130177515) and add it to both sides. Add '0.2130177515' to each side of the equation. -0.9230769231x + 0.2130177515 + x2 = 1.307692308 + 0.2130177515 Reorder the terms: 0.2130177515 + -0.9230769231x + x2 = 1.307692308 + 0.2130177515 Combine like terms: 1.307692308 + 0.2130177515 = 1.5207100595 0.2130177515 + -0.9230769231x + x2 = 1.5207100595 Factor a perfect square on the left side: (x + -0.4615384616)(x + -0.4615384616) = 1.5207100595 Calculate the square root of the right side: 1.233170734 Break this problem into two subproblems by setting (x + -0.4615384616) equal to 1.233170734 and -1.233170734.Subproblem 1
x + -0.4615384616 = 1.233170734 Simplifying x + -0.4615384616 = 1.233170734 Reorder the terms: -0.4615384616 + x = 1.233170734 Solving -0.4615384616 + x = 1.233170734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4615384616' to each side of the equation. -0.4615384616 + 0.4615384616 + x = 1.233170734 + 0.4615384616 Combine like terms: -0.4615384616 + 0.4615384616 = 0.0000000000 0.0000000000 + x = 1.233170734 + 0.4615384616 x = 1.233170734 + 0.4615384616 Combine like terms: 1.233170734 + 0.4615384616 = 1.6947091956 x = 1.6947091956 Simplifying x = 1.6947091956Subproblem 2
x + -0.4615384616 = -1.233170734 Simplifying x + -0.4615384616 = -1.233170734 Reorder the terms: -0.4615384616 + x = -1.233170734 Solving -0.4615384616 + x = -1.233170734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4615384616' to each side of the equation. -0.4615384616 + 0.4615384616 + x = -1.233170734 + 0.4615384616 Combine like terms: -0.4615384616 + 0.4615384616 = 0.0000000000 0.0000000000 + x = -1.233170734 + 0.4615384616 x = -1.233170734 + 0.4615384616 Combine like terms: -1.233170734 + 0.4615384616 = -0.7716322724 x = -0.7716322724 Simplifying x = -0.7716322724Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6947091956, -0.7716322724}
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