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Simplifying 0 = 12x2 + 84x + 7 Reorder the terms: 0 = 7 + 84x + 12x2 Solving 0 = 7 + 84x + 12x2 Solving for variable 'x'. Combine like terms: 0 + -7 = -7 -7 + -84x + -12x2 = 7 + 84x + 12x2 + -7 + -84x + -12x2 Reorder the terms: -7 + -84x + -12x2 = 7 + -7 + 84x + -84x + 12x2 + -12x2 Combine like terms: 7 + -7 = 0 -7 + -84x + -12x2 = 0 + 84x + -84x + 12x2 + -12x2 -7 + -84x + -12x2 = 84x + -84x + 12x2 + -12x2 Combine like terms: 84x + -84x = 0 -7 + -84x + -12x2 = 0 + 12x2 + -12x2 -7 + -84x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -7 + -84x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 84x + 12x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 84x + 12x2)' equal to zero and attempt to solve: Simplifying 7 + 84x + 12x2 = 0 Solving 7 + 84x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.5833333333 + 7x + x2 = 0 Move the constant term to the right: Add '-0.5833333333' to each side of the equation. 0.5833333333 + 7x + -0.5833333333 + x2 = 0 + -0.5833333333 Reorder the terms: 0.5833333333 + -0.5833333333 + 7x + x2 = 0 + -0.5833333333 Combine like terms: 0.5833333333 + -0.5833333333 = 0.0000000000 0.0000000000 + 7x + x2 = 0 + -0.5833333333 7x + x2 = 0 + -0.5833333333 Combine like terms: 0 + -0.5833333333 = -0.5833333333 7x + x2 = -0.5833333333 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -0.5833333333 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -0.5833333333 + 12.25 Combine like terms: -0.5833333333 + 12.25 = 11.6666666667 12.25 + 7x + x2 = 11.6666666667 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 11.6666666667 Calculate the square root of the right side: 3.415650255 Break this problem into two subproblems by setting (x + 3.5) equal to 3.415650255 and -3.415650255.Subproblem 1
x + 3.5 = 3.415650255 Simplifying x + 3.5 = 3.415650255 Reorder the terms: 3.5 + x = 3.415650255 Solving 3.5 + x = 3.415650255 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 3.415650255 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.415650255 + -3.5 x = 3.415650255 + -3.5 Combine like terms: 3.415650255 + -3.5 = -0.084349745 x = -0.084349745 Simplifying x = -0.084349745Subproblem 2
x + 3.5 = -3.415650255 Simplifying x + 3.5 = -3.415650255 Reorder the terms: 3.5 + x = -3.415650255 Solving 3.5 + x = -3.415650255 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -3.415650255 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.415650255 + -3.5 x = -3.415650255 + -3.5 Combine like terms: -3.415650255 + -3.5 = -6.915650255 x = -6.915650255 Simplifying x = -6.915650255Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.084349745, -6.915650255}Solution
x = {-0.084349745, -6.915650255}
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