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Simplifying 2x2 + 16x = 42 Reorder the terms: 16x + 2x2 = 42 Solving 16x + 2x2 = 42 Solving for variable 'x'. Reorder the terms: -42 + 16x + 2x2 = 42 + -42 Combine like terms: 42 + -42 = 0 -42 + 16x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + 8x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-21 + 8x + x2)' equal to zero and attempt to solve: Simplifying -21 + 8x + x2 = 0 Solving -21 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + 8x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + 8x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 8x + x2 = 0 + 21 8x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 8x + x2 = 21 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 21 + 16 Reorder the terms: 16 + 8x + x2 = 21 + 16 Combine like terms: 21 + 16 = 37 16 + 8x + x2 = 37 Factor a perfect square on the left side: (x + 4)(x + 4) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (x + 4) equal to 6.08276253 and -6.08276253.Subproblem 1
x + 4 = 6.08276253 Simplifying x + 4 = 6.08276253 Reorder the terms: 4 + x = 6.08276253 Solving 4 + x = 6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 6.08276253 + -4 Combine like terms: 4 + -4 = 0 0 + x = 6.08276253 + -4 x = 6.08276253 + -4 Combine like terms: 6.08276253 + -4 = 2.08276253 x = 2.08276253 Simplifying x = 2.08276253Subproblem 2
x + 4 = -6.08276253 Simplifying x + 4 = -6.08276253 Reorder the terms: 4 + x = -6.08276253 Solving 4 + x = -6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -6.08276253 + -4 Combine like terms: 4 + -4 = 0 0 + x = -6.08276253 + -4 x = -6.08276253 + -4 Combine like terms: -6.08276253 + -4 = -10.08276253 x = -10.08276253 Simplifying x = -10.08276253Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.08276253, -10.08276253}Solution
x = {2.08276253, -10.08276253}
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