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Simplifying 20x2 + 24x + -96 = 0 Reorder the terms: -96 + 24x + 20x2 = 0 Solving -96 + 24x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-24 + 6x + 5x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-24 + 6x + 5x2)' equal to zero and attempt to solve: Simplifying -24 + 6x + 5x2 = 0 Solving -24 + 6x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.8 + 1.2x + x2 = 0 Move the constant term to the right: Add '4.8' to each side of the equation. -4.8 + 1.2x + 4.8 + x2 = 0 + 4.8 Reorder the terms: -4.8 + 4.8 + 1.2x + x2 = 0 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + 1.2x + x2 = 0 + 4.8 1.2x + x2 = 0 + 4.8 Combine like terms: 0 + 4.8 = 4.8 1.2x + x2 = 4.8 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x2 = 4.8 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 4.8 + 0.36 Combine like terms: 4.8 + 0.36 = 5.16 0.36 + 1.2x + x2 = 5.16 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 5.16 Calculate the square root of the right side: 2.271563338 Break this problem into two subproblems by setting (x + 0.6) equal to 2.271563338 and -2.271563338.Subproblem 1
x + 0.6 = 2.271563338 Simplifying x + 0.6 = 2.271563338 Reorder the terms: 0.6 + x = 2.271563338 Solving 0.6 + x = 2.271563338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 2.271563338 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 2.271563338 + -0.6 x = 2.271563338 + -0.6 Combine like terms: 2.271563338 + -0.6 = 1.671563338 x = 1.671563338 Simplifying x = 1.671563338Subproblem 2
x + 0.6 = -2.271563338 Simplifying x + 0.6 = -2.271563338 Reorder the terms: 0.6 + x = -2.271563338 Solving 0.6 + x = -2.271563338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -2.271563338 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -2.271563338 + -0.6 x = -2.271563338 + -0.6 Combine like terms: -2.271563338 + -0.6 = -2.871563338 x = -2.871563338 Simplifying x = -2.871563338Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.671563338, -2.871563338}Solution
x = {1.671563338, -2.871563338}
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