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Simplifying 6x2 + 3x + 12 = 20 Reorder the terms: 12 + 3x + 6x2 = 20 Solving 12 + 3x + 6x2 = 20 Solving for variable 'x'. Reorder the terms: 12 + -20 + 3x + 6x2 = 20 + -20 Combine like terms: 12 + -20 = -8 -8 + 3x + 6x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -8 + 3x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.333333333 + 0.5x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 0.5x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 0.5x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 0.5x + x2 = 0 + 1.333333333 0.5x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 0.5x + x2 = 1.333333333 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 1.333333333 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 1.333333333 + 0.0625 Combine like terms: 1.333333333 + 0.0625 = 1.395833333 0.0625 + 0.5x + x2 = 1.395833333 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 1.395833333 Calculate the square root of the right side: 1.181453906 Break this problem into two subproblems by setting (x + 0.25) equal to 1.181453906 and -1.181453906.Subproblem 1
x + 0.25 = 1.181453906 Simplifying x + 0.25 = 1.181453906 Reorder the terms: 0.25 + x = 1.181453906 Solving 0.25 + x = 1.181453906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.181453906 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.181453906 + -0.25 x = 1.181453906 + -0.25 Combine like terms: 1.181453906 + -0.25 = 0.931453906 x = 0.931453906 Simplifying x = 0.931453906Subproblem 2
x + 0.25 = -1.181453906 Simplifying x + 0.25 = -1.181453906 Reorder the terms: 0.25 + x = -1.181453906 Solving 0.25 + x = -1.181453906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.181453906 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.181453906 + -0.25 x = -1.181453906 + -0.25 Combine like terms: -1.181453906 + -0.25 = -1.431453906 x = -1.431453906 Simplifying x = -1.431453906Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.931453906, -1.431453906}
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