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Simplifying 12x2 + 9x + -8 = 0 Reorder the terms: -8 + 9x + 12x2 = 0 Solving -8 + 9x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.6666666667 + 0.75x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 0.75x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 0.75x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 0.75x + x2 = 0 + 0.6666666667 0.75x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 0.75x + x2 = 0.6666666667 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 0.6666666667 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 0.6666666667 + 0.140625 Combine like terms: 0.6666666667 + 0.140625 = 0.8072916667 0.140625 + 0.75x + x2 = 0.8072916667 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 0.8072916667 Calculate the square root of the right side: 0.898494111 Break this problem into two subproblems by setting (x + 0.375) equal to 0.898494111 and -0.898494111.Subproblem 1
x + 0.375 = 0.898494111 Simplifying x + 0.375 = 0.898494111 Reorder the terms: 0.375 + x = 0.898494111 Solving 0.375 + x = 0.898494111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 0.898494111 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 0.898494111 + -0.375 x = 0.898494111 + -0.375 Combine like terms: 0.898494111 + -0.375 = 0.523494111 x = 0.523494111 Simplifying x = 0.523494111Subproblem 2
x + 0.375 = -0.898494111 Simplifying x + 0.375 = -0.898494111 Reorder the terms: 0.375 + x = -0.898494111 Solving 0.375 + x = -0.898494111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -0.898494111 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -0.898494111 + -0.375 x = -0.898494111 + -0.375 Combine like terms: -0.898494111 + -0.375 = -1.273494111 x = -1.273494111 Simplifying x = -1.273494111Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.523494111, -1.273494111}
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