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Simplifying 15x2 + -144x + -48 = 0 Reorder the terms: -48 + -144x + 15x2 = 0 Solving -48 + -144x + 15x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-16 + -48x + 5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-16 + -48x + 5x2)' equal to zero and attempt to solve: Simplifying -16 + -48x + 5x2 = 0 Solving -16 + -48x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.2 + -9.6x + x2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + -9.6x + 3.2 + x2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + -9.6x + x2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + -9.6x + x2 = 0 + 3.2 -9.6x + x2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 -9.6x + x2 = 3.2 The x term is -9.6x. Take half its coefficient (-4.8). Square it (23.04) and add it to both sides. Add '23.04' to each side of the equation. -9.6x + 23.04 + x2 = 3.2 + 23.04 Reorder the terms: 23.04 + -9.6x + x2 = 3.2 + 23.04 Combine like terms: 3.2 + 23.04 = 26.24 23.04 + -9.6x + x2 = 26.24 Factor a perfect square on the left side: (x + -4.8)(x + -4.8) = 26.24 Calculate the square root of the right side: 5.12249939 Break this problem into two subproblems by setting (x + -4.8) equal to 5.12249939 and -5.12249939.Subproblem 1
x + -4.8 = 5.12249939 Simplifying x + -4.8 = 5.12249939 Reorder the terms: -4.8 + x = 5.12249939 Solving -4.8 + x = 5.12249939 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.8' to each side of the equation. -4.8 + 4.8 + x = 5.12249939 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + x = 5.12249939 + 4.8 x = 5.12249939 + 4.8 Combine like terms: 5.12249939 + 4.8 = 9.92249939 x = 9.92249939 Simplifying x = 9.92249939Subproblem 2
x + -4.8 = -5.12249939 Simplifying x + -4.8 = -5.12249939 Reorder the terms: -4.8 + x = -5.12249939 Solving -4.8 + x = -5.12249939 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.8' to each side of the equation. -4.8 + 4.8 + x = -5.12249939 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + x = -5.12249939 + 4.8 x = -5.12249939 + 4.8 Combine like terms: -5.12249939 + 4.8 = -0.32249939 x = -0.32249939 Simplifying x = -0.32249939Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.92249939, -0.32249939}Solution
x = {9.92249939, -0.32249939}
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