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Simplifying (3x * 3x) + 5x + -6 = 0 Reorder the terms for easier multiplication: (3 * 3x * x) + 5x + -6 = 0 Multiply 3 * 3 (9x * x) + 5x + -6 = 0 Multiply x * x (9x2) + 5x + -6 = 0 Reorder the terms: -6 + 5x + (9x2) = 0 Solving -6 + 5x + (9x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.6666666667 + 0.5555555556x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 0.5555555556x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 0.5555555556x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 0.5555555556x + x2 = 0 + 0.6666666667 0.5555555556x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 0.5555555556x + x2 = 0.6666666667 The x term is 0.5555555556x. Take half its coefficient (0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. 0.5555555556x + 0.07716049384 + x2 = 0.6666666667 + 0.07716049384 Reorder the terms: 0.07716049384 + 0.5555555556x + x2 = 0.6666666667 + 0.07716049384 Combine like terms: 0.6666666667 + 0.07716049384 = 0.74382716054 0.07716049384 + 0.5555555556x + x2 = 0.74382716054 Factor a perfect square on the left side: ((x) + 0.2777777778)((x) + 0.2777777778) = 0.74382716054 Calculate the square root of the right side: 0.86245415 Break this problem into two subproblems by setting ((x) + 0.2777777778) equal to 0.86245415 and -0.86245415.Subproblem 1
(x) + 0.2777777778 = 0.86245415 Simplifying (x) + 0.2777777778 = 0.86245415 x + 0.2777777778 = 0.86245415 Reorder the terms: 0.2777777778 + x = 0.86245415 Solving 0.2777777778 + x = 0.86245415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = 0.86245415 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = 0.86245415 + -0.2777777778 x = 0.86245415 + -0.2777777778 Combine like terms: 0.86245415 + -0.2777777778 = 0.5846763722 x = 0.5846763722 Simplifying x = 0.5846763722Subproblem 2
(x) + 0.2777777778 = -0.86245415 Simplifying (x) + 0.2777777778 = -0.86245415 x + 0.2777777778 = -0.86245415 Reorder the terms: 0.2777777778 + x = -0.86245415 Solving 0.2777777778 + x = -0.86245415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = -0.86245415 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = -0.86245415 + -0.2777777778 x = -0.86245415 + -0.2777777778 Combine like terms: -0.86245415 + -0.2777777778 = -1.1402319278 x = -1.1402319278 Simplifying x = -1.1402319278Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5846763722, -1.1402319278}
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