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Simplifying 3x2 + -12x + 9 = 5x + -4x2 Reorder the terms: 9 + -12x + 3x2 = 5x + -4x2 Solving 9 + -12x + 3x2 = 5x + -4x2 Solving for variable 'x'. Reorder the terms: 9 + -12x + -5x + 3x2 + 4x2 = 5x + -4x2 + -5x + 4x2 Combine like terms: -12x + -5x = -17x 9 + -17x + 3x2 + 4x2 = 5x + -4x2 + -5x + 4x2 Combine like terms: 3x2 + 4x2 = 7x2 9 + -17x + 7x2 = 5x + -4x2 + -5x + 4x2 Reorder the terms: 9 + -17x + 7x2 = 5x + -5x + -4x2 + 4x2 Combine like terms: 5x + -5x = 0 9 + -17x + 7x2 = 0 + -4x2 + 4x2 9 + -17x + 7x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 9 + -17x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.285714286 + -2.428571429x + x2 = 0 Move the constant term to the right: Add '-1.285714286' to each side of the equation. 1.285714286 + -2.428571429x + -1.285714286 + x2 = 0 + -1.285714286 Reorder the terms: 1.285714286 + -1.285714286 + -2.428571429x + x2 = 0 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + -2.428571429x + x2 = 0 + -1.285714286 -2.428571429x + x2 = 0 + -1.285714286 Combine like terms: 0 + -1.285714286 = -1.285714286 -2.428571429x + x2 = -1.285714286 The x term is -2.428571429x. Take half its coefficient (-1.214285715). Square it (1.474489798) and add it to both sides. Add '1.474489798' to each side of the equation. -2.428571429x + 1.474489798 + x2 = -1.285714286 + 1.474489798 Reorder the terms: 1.474489798 + -2.428571429x + x2 = -1.285714286 + 1.474489798 Combine like terms: -1.285714286 + 1.474489798 = 0.188775512 1.474489798 + -2.428571429x + x2 = 0.188775512 Factor a perfect square on the left side: (x + -1.214285715)(x + -1.214285715) = 0.188775512 Calculate the square root of the right side: 0.43448304 Break this problem into two subproblems by setting (x + -1.214285715) equal to 0.43448304 and -0.43448304.Subproblem 1
x + -1.214285715 = 0.43448304 Simplifying x + -1.214285715 = 0.43448304 Reorder the terms: -1.214285715 + x = 0.43448304 Solving -1.214285715 + x = 0.43448304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.214285715' to each side of the equation. -1.214285715 + 1.214285715 + x = 0.43448304 + 1.214285715 Combine like terms: -1.214285715 + 1.214285715 = 0.000000000 0.000000000 + x = 0.43448304 + 1.214285715 x = 0.43448304 + 1.214285715 Combine like terms: 0.43448304 + 1.214285715 = 1.648768755 x = 1.648768755 Simplifying x = 1.648768755Subproblem 2
x + -1.214285715 = -0.43448304 Simplifying x + -1.214285715 = -0.43448304 Reorder the terms: -1.214285715 + x = -0.43448304 Solving -1.214285715 + x = -0.43448304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.214285715' to each side of the equation. -1.214285715 + 1.214285715 + x = -0.43448304 + 1.214285715 Combine like terms: -1.214285715 + 1.214285715 = 0.000000000 0.000000000 + x = -0.43448304 + 1.214285715 x = -0.43448304 + 1.214285715 Combine like terms: -0.43448304 + 1.214285715 = 0.779802675 x = 0.779802675 Simplifying x = 0.779802675Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.648768755, 0.779802675}
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