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Simplifying 4x2 + -12x + -92 = 0 Reorder the terms: -92 + -12x + 4x2 = 0 Solving -92 + -12x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-23 + -3x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-23 + -3x + x2)' equal to zero and attempt to solve: Simplifying -23 + -3x + x2 = 0 Solving -23 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + -3x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + -3x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -3x + x2 = 0 + 23 -3x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 -3x + x2 = 23 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 = 23 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 23 + 2.25 Combine like terms: 23 + 2.25 = 25.25 2.25 + -3x + x2 = 25.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 25.25 Calculate the square root of the right side: 5.024937811 Break this problem into two subproblems by setting (x + -1.5) equal to 5.024937811 and -5.024937811.Subproblem 1
x + -1.5 = 5.024937811 Simplifying x + -1.5 = 5.024937811 Reorder the terms: -1.5 + x = 5.024937811 Solving -1.5 + x = 5.024937811 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 = 5.024937811 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 5.024937811 + 1.5 x = 5.024937811 + 1.5 Combine like terms: 5.024937811 + 1.5 = 6.524937811 x = 6.524937811 Simplifying x = 6.524937811Subproblem 2
x + -1.5 = -5.024937811 Simplifying x + -1.5 = -5.024937811 Reorder the terms: -1.5 + x = -5.024937811 Solving -1.5 + x = -5.024937811 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 = -5.024937811 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -5.024937811 + 1.5 x = -5.024937811 + 1.5 Combine like terms: -5.024937811 + 1.5 = -3.524937811 x = -3.524937811 Simplifying x = -3.524937811Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.524937811, -3.524937811}Solution
x = {6.524937811, -3.524937811}
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