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Simplifying 12x2 + -96x + 135 = 0 Reorder the terms: 135 + -96x + 12x2 = 0 Solving 135 + -96x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(45 + -32x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(45 + -32x + 4x2)' equal to zero and attempt to solve: Simplifying 45 + -32x + 4x2 = 0 Solving 45 + -32x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 11.25 + -8x + x2 = 0 Move the constant term to the right: Add '-11.25' to each side of the equation. 11.25 + -8x + -11.25 + x2 = 0 + -11.25 Reorder the terms: 11.25 + -11.25 + -8x + x2 = 0 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + -8x + x2 = 0 + -11.25 -8x + x2 = 0 + -11.25 Combine like terms: 0 + -11.25 = -11.25 -8x + x2 = -11.25 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -11.25 + 16 Reorder the terms: 16 + -8x + x2 = -11.25 + 16 Combine like terms: -11.25 + 16 = 4.75 16 + -8x + x2 = 4.75 Factor a perfect square on the left side: (x + -4)(x + -4) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (x + -4) equal to 2.179449472 and -2.179449472.Subproblem 1
x + -4 = 2.179449472 Simplifying x + -4 = 2.179449472 Reorder the terms: -4 + x = 2.179449472 Solving -4 + x = 2.179449472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 2.179449472 + 4 Combine like terms: -4 + 4 = 0 0 + x = 2.179449472 + 4 x = 2.179449472 + 4 Combine like terms: 2.179449472 + 4 = 6.179449472 x = 6.179449472 Simplifying x = 6.179449472Subproblem 2
x + -4 = -2.179449472 Simplifying x + -4 = -2.179449472 Reorder the terms: -4 + x = -2.179449472 Solving -4 + x = -2.179449472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -2.179449472 + 4 Combine like terms: -4 + 4 = 0 0 + x = -2.179449472 + 4 x = -2.179449472 + 4 Combine like terms: -2.179449472 + 4 = 1.820550528 x = 1.820550528 Simplifying x = 1.820550528Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.179449472, 1.820550528}Solution
x = {6.179449472, 1.820550528}
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