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Simplifying 2x2 + 4x = 480 Reorder the terms: 4x + 2x2 = 480 Solving 4x + 2x2 = 480 Solving for variable 'x'. Reorder the terms: -480 + 4x + 2x2 = 480 + -480 Combine like terms: 480 + -480 = 0 -480 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-240 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-240 + 2x + x2)' equal to zero and attempt to solve: Simplifying -240 + 2x + x2 = 0 Solving -240 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '240' to each side of the equation. -240 + 2x + 240 + x2 = 0 + 240 Reorder the terms: -240 + 240 + 2x + x2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + 2x + x2 = 0 + 240 2x + x2 = 0 + 240 Combine like terms: 0 + 240 = 240 2x + x2 = 240 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 240 + 1 Reorder the terms: 1 + 2x + x2 = 240 + 1 Combine like terms: 240 + 1 = 241 1 + 2x + x2 = 241 Factor a perfect square on the left side: (x + 1)(x + 1) = 241 Calculate the square root of the right side: 15.524174696 Break this problem into two subproblems by setting (x + 1) equal to 15.524174696 and -15.524174696.Subproblem 1
x + 1 = 15.524174696 Simplifying x + 1 = 15.524174696 Reorder the terms: 1 + x = 15.524174696 Solving 1 + x = 15.524174696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 15.524174696 + -1 Combine like terms: 1 + -1 = 0 0 + x = 15.524174696 + -1 x = 15.524174696 + -1 Combine like terms: 15.524174696 + -1 = 14.524174696 x = 14.524174696 Simplifying x = 14.524174696Subproblem 2
x + 1 = -15.524174696 Simplifying x + 1 = -15.524174696 Reorder the terms: 1 + x = -15.524174696 Solving 1 + x = -15.524174696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -15.524174696 + -1 Combine like terms: 1 + -1 = 0 0 + x = -15.524174696 + -1 x = -15.524174696 + -1 Combine like terms: -15.524174696 + -1 = -16.524174696 x = -16.524174696 Simplifying x = -16.524174696Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.524174696, -16.524174696}Solution
x = {14.524174696, -16.524174696}
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