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Simplifying 2x2 + 8x + -24 = 960 Reorder the terms: -24 + 8x + 2x2 = 960 Solving -24 + 8x + 2x2 = 960 Solving for variable 'x'. Reorder the terms: -24 + -960 + 8x + 2x2 = 960 + -960 Combine like terms: -24 + -960 = -984 -984 + 8x + 2x2 = 960 + -960 Combine like terms: 960 + -960 = 0 -984 + 8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-492 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-492 + 4x + x2)' equal to zero and attempt to solve: Simplifying -492 + 4x + x2 = 0 Solving -492 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '492' to each side of the equation. -492 + 4x + 492 + x2 = 0 + 492 Reorder the terms: -492 + 492 + 4x + x2 = 0 + 492 Combine like terms: -492 + 492 = 0 0 + 4x + x2 = 0 + 492 4x + x2 = 0 + 492 Combine like terms: 0 + 492 = 492 4x + x2 = 492 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 492 + 4 Reorder the terms: 4 + 4x + x2 = 492 + 4 Combine like terms: 492 + 4 = 496 4 + 4x + x2 = 496 Factor a perfect square on the left side: (x + 2)(x + 2) = 496 Calculate the square root of the right side: 22.271057451 Break this problem into two subproblems by setting (x + 2) equal to 22.271057451 and -22.271057451.Subproblem 1
x + 2 = 22.271057451 Simplifying x + 2 = 22.271057451 Reorder the terms: 2 + x = 22.271057451 Solving 2 + x = 22.271057451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 22.271057451 + -2 Combine like terms: 2 + -2 = 0 0 + x = 22.271057451 + -2 x = 22.271057451 + -2 Combine like terms: 22.271057451 + -2 = 20.271057451 x = 20.271057451 Simplifying x = 20.271057451Subproblem 2
x + 2 = -22.271057451 Simplifying x + 2 = -22.271057451 Reorder the terms: 2 + x = -22.271057451 Solving 2 + x = -22.271057451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -22.271057451 + -2 Combine like terms: 2 + -2 = 0 0 + x = -22.271057451 + -2 x = -22.271057451 + -2 Combine like terms: -22.271057451 + -2 = -24.271057451 x = -24.271057451 Simplifying x = -24.271057451Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.271057451, -24.271057451}Solution
x = {20.271057451, -24.271057451}
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