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Simplifying 12x2 + -72x + 45 = 0 Reorder the terms: 45 + -72x + 12x2 = 0 Solving 45 + -72x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(15 + -24x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(15 + -24x + 4x2)' equal to zero and attempt to solve: Simplifying 15 + -24x + 4x2 = 0 Solving 15 + -24x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.75 + -6x + x2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + -6x + -3.75 + x2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + -6x + x2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + -6x + x2 = 0 + -3.75 -6x + x2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 -6x + x2 = -3.75 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -3.75 + 9 Reorder the terms: 9 + -6x + x2 = -3.75 + 9 Combine like terms: -3.75 + 9 = 5.25 9 + -6x + x2 = 5.25 Factor a perfect square on the left side: (x + -3)(x + -3) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x + -3) equal to 2.291287847 and -2.291287847.Subproblem 1
x + -3 = 2.291287847 Simplifying x + -3 = 2.291287847 Reorder the terms: -3 + x = 2.291287847 Solving -3 + x = 2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.291287847 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.291287847 + 3 x = 2.291287847 + 3 Combine like terms: 2.291287847 + 3 = 5.291287847 x = 5.291287847 Simplifying x = 5.291287847Subproblem 2
x + -3 = -2.291287847 Simplifying x + -3 = -2.291287847 Reorder the terms: -3 + x = -2.291287847 Solving -3 + x = -2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.291287847 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.291287847 + 3 x = -2.291287847 + 3 Combine like terms: -2.291287847 + 3 = 0.708712153 x = 0.708712153 Simplifying x = 0.708712153Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.291287847, 0.708712153}Solution
x = {5.291287847, 0.708712153}
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