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Simplifying 12 = 2x2 + 6x Reorder the terms: 12 = 6x + 2x2 Solving 12 = 6x + 2x2 Solving for variable 'x'. Reorder the terms: 12 + -6x + -2x2 = 6x + -6x + 2x2 + -2x2 Combine like terms: 6x + -6x = 0 12 + -6x + -2x2 = 0 + 2x2 + -2x2 12 + -6x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 12 + -6x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -3x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + -3x + -1x2)' equal to zero and attempt to solve: Simplifying 6 + -3x + -1x2 = 0 Solving 6 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -6 + 3x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 3x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 3x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 3x + x2 = 0 + 6 3x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 3x + x2 = 6 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 6 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 6 + 2.25 Combine like terms: 6 + 2.25 = 8.25 2.25 + 3x + x2 = 8.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (x + 1.5) equal to 2.872281323 and -2.872281323.Subproblem 1
x + 1.5 = 2.872281323 Simplifying x + 1.5 = 2.872281323 Reorder the terms: 1.5 + x = 2.872281323 Solving 1.5 + x = 2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.872281323 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.872281323 + -1.5 x = 2.872281323 + -1.5 Combine like terms: 2.872281323 + -1.5 = 1.372281323 x = 1.372281323 Simplifying x = 1.372281323Subproblem 2
x + 1.5 = -2.872281323 Simplifying x + 1.5 = -2.872281323 Reorder the terms: 1.5 + x = -2.872281323 Solving 1.5 + x = -2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.872281323 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.872281323 + -1.5 x = -2.872281323 + -1.5 Combine like terms: -2.872281323 + -1.5 = -4.372281323 x = -4.372281323 Simplifying x = -4.372281323Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.372281323, -4.372281323}Solution
x = {1.372281323, -4.372281323}
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