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Simplifying 4x2 + -22x + -96 = 0 Reorder the terms: -96 + -22x + 4x2 = 0 Solving -96 + -22x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-48 + -11x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-48 + -11x + 2x2)' equal to zero and attempt to solve: Simplifying -48 + -11x + 2x2 = 0 Solving -48 + -11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -24 + -5.5x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + -5.5x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -5.5x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -5.5x + x2 = 0 + 24 -5.5x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -5.5x + x2 = 24 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = 24 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = 24 + 7.5625 Combine like terms: 24 + 7.5625 = 31.5625 7.5625 + -5.5x + x2 = 31.5625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 31.5625 Calculate the square root of the right side: 5.618051264 Break this problem into two subproblems by setting (x + -2.75) equal to 5.618051264 and -5.618051264.Subproblem 1
x + -2.75 = 5.618051264 Simplifying x + -2.75 = 5.618051264 Reorder the terms: -2.75 + x = 5.618051264 Solving -2.75 + x = 5.618051264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 5.618051264 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 5.618051264 + 2.75 x = 5.618051264 + 2.75 Combine like terms: 5.618051264 + 2.75 = 8.368051264 x = 8.368051264 Simplifying x = 8.368051264Subproblem 2
x + -2.75 = -5.618051264 Simplifying x + -2.75 = -5.618051264 Reorder the terms: -2.75 + x = -5.618051264 Solving -2.75 + x = -5.618051264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -5.618051264 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -5.618051264 + 2.75 x = -5.618051264 + 2.75 Combine like terms: -5.618051264 + 2.75 = -2.868051264 x = -2.868051264 Simplifying x = -2.868051264Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.368051264, -2.868051264}Solution
x = {8.368051264, -2.868051264}
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