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Simplifying 12x2 + -84x + 48 = 0 Reorder the terms: 48 + -84x + 12x2 = 0 Solving 48 + -84x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(4 + -7x + x2) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(4 + -7x + x2)' equal to zero and attempt to solve: Simplifying 4 + -7x + x2 = 0 Solving 4 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -7x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -7x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7x + x2 = 0 + -4 -7x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -7x + x2 = -4 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 = -4 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -4 + 12.25 Combine like terms: -4 + 12.25 = 8.25 12.25 + -7x + x2 = 8.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (x + -3.5) equal to 2.872281323 and -2.872281323.Subproblem 1
x + -3.5 = 2.872281323 Simplifying x + -3.5 = 2.872281323 Reorder the terms: -3.5 + x = 2.872281323 Solving -3.5 + x = 2.872281323 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 = 2.872281323 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 2.872281323 + 3.5 x = 2.872281323 + 3.5 Combine like terms: 2.872281323 + 3.5 = 6.372281323 x = 6.372281323 Simplifying x = 6.372281323Subproblem 2
x + -3.5 = -2.872281323 Simplifying x + -3.5 = -2.872281323 Reorder the terms: -3.5 + x = -2.872281323 Solving -3.5 + x = -2.872281323 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 = -2.872281323 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -2.872281323 + 3.5 x = -2.872281323 + 3.5 Combine like terms: -2.872281323 + 3.5 = 0.627718677 x = 0.627718677 Simplifying x = 0.627718677Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.372281323, 0.627718677}Solution
x = {6.372281323, 0.627718677}
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