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Simplifying 12x2 + -84x + 9 = 0 Reorder the terms: 9 + -84x + 12x2 = 0 Solving 9 + -84x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -28x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -28x + 4x2)' equal to zero and attempt to solve: Simplifying 3 + -28x + 4x2 = 0 Solving 3 + -28x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + -7x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -7x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -7x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -7x + x2 = 0 + -0.75 -7x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -7x + x2 = -0.75 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 = -0.75 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -0.75 + 12.25 Combine like terms: -0.75 + 12.25 = 11.5 12.25 + -7x + x2 = 11.5 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 11.5 Calculate the square root of the right side: 3.391164992 Break this problem into two subproblems by setting (x + -3.5) equal to 3.391164992 and -3.391164992.Subproblem 1
x + -3.5 = 3.391164992 Simplifying x + -3.5 = 3.391164992 Reorder the terms: -3.5 + x = 3.391164992 Solving -3.5 + x = 3.391164992 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 = 3.391164992 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.391164992 + 3.5 x = 3.391164992 + 3.5 Combine like terms: 3.391164992 + 3.5 = 6.891164992 x = 6.891164992 Simplifying x = 6.891164992Subproblem 2
x + -3.5 = -3.391164992 Simplifying x + -3.5 = -3.391164992 Reorder the terms: -3.5 + x = -3.391164992 Solving -3.5 + x = -3.391164992 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 = -3.391164992 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.391164992 + 3.5 x = -3.391164992 + 3.5 Combine like terms: -3.391164992 + 3.5 = 0.108835008 x = 0.108835008 Simplifying x = 0.108835008Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.891164992, 0.108835008}Solution
x = {6.891164992, 0.108835008}
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