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Simplifying 12x2 + -84x + 2 = 0 Reorder the terms: 2 + -84x + 12x2 = 0 Solving 2 + -84x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -42x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -42x + 6x2)' equal to zero and attempt to solve: Simplifying 1 + -42x + 6x2 = 0 Solving 1 + -42x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.1666666667 + -7x + x2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + -7x + -0.1666666667 + x2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + -7x + x2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + -7x + x2 = 0 + -0.1666666667 -7x + x2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 -7x + x2 = -0.1666666667 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 = -0.1666666667 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -0.1666666667 + 12.25 Combine like terms: -0.1666666667 + 12.25 = 12.0833333333 12.25 + -7x + x2 = 12.0833333333 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 12.0833333333 Calculate the square root of the right side: 3.476108936 Break this problem into two subproblems by setting (x + -3.5) equal to 3.476108936 and -3.476108936.Subproblem 1
x + -3.5 = 3.476108936 Simplifying x + -3.5 = 3.476108936 Reorder the terms: -3.5 + x = 3.476108936 Solving -3.5 + x = 3.476108936 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 = 3.476108936 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.476108936 + 3.5 x = 3.476108936 + 3.5 Combine like terms: 3.476108936 + 3.5 = 6.976108936 x = 6.976108936 Simplifying x = 6.976108936Subproblem 2
x + -3.5 = -3.476108936 Simplifying x + -3.5 = -3.476108936 Reorder the terms: -3.5 + x = -3.476108936 Solving -3.5 + x = -3.476108936 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 = -3.476108936 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.476108936 + 3.5 x = -3.476108936 + 3.5 Combine like terms: -3.476108936 + 3.5 = 0.023891064 x = 0.023891064 Simplifying x = 0.023891064Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.976108936, 0.023891064}Solution
x = {6.976108936, 0.023891064}
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