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Simplifying 24x2 + -72x + -105 = 0 Reorder the terms: -105 + -72x + 24x2 = 0 Solving -105 + -72x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-35 + -24x + 8x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-35 + -24x + 8x2)' equal to zero and attempt to solve: Simplifying -35 + -24x + 8x2 = 0 Solving -35 + -24x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -4.375 + -3x + x2 = 0 Move the constant term to the right: Add '4.375' to each side of the equation. -4.375 + -3x + 4.375 + x2 = 0 + 4.375 Reorder the terms: -4.375 + 4.375 + -3x + x2 = 0 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + -3x + x2 = 0 + 4.375 -3x + x2 = 0 + 4.375 Combine like terms: 0 + 4.375 = 4.375 -3x + x2 = 4.375 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 = 4.375 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 4.375 + 2.25 Combine like terms: 4.375 + 2.25 = 6.625 2.25 + -3x + x2 = 6.625 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 6.625 Calculate the square root of the right side: 2.573907535 Break this problem into two subproblems by setting (x + -1.5) equal to 2.573907535 and -2.573907535.Subproblem 1
x + -1.5 = 2.573907535 Simplifying x + -1.5 = 2.573907535 Reorder the terms: -1.5 + x = 2.573907535 Solving -1.5 + x = 2.573907535 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 = 2.573907535 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.573907535 + 1.5 x = 2.573907535 + 1.5 Combine like terms: 2.573907535 + 1.5 = 4.073907535 x = 4.073907535 Simplifying x = 4.073907535Subproblem 2
x + -1.5 = -2.573907535 Simplifying x + -1.5 = -2.573907535 Reorder the terms: -1.5 + x = -2.573907535 Solving -1.5 + x = -2.573907535 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 = -2.573907535 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.573907535 + 1.5 x = -2.573907535 + 1.5 Combine like terms: -2.573907535 + 1.5 = -1.073907535 x = -1.073907535 Simplifying x = -1.073907535Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.073907535, -1.073907535}Solution
x = {4.073907535, -1.073907535}
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