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Simplifying 2x2 + 16x + -400 = 0 Reorder the terms: -400 + 16x + 2x2 = 0 Solving -400 + 16x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-200 + 8x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-200 + 8x + x2)' equal to zero and attempt to solve: Simplifying -200 + 8x + x2 = 0 Solving -200 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '200' to each side of the equation. -200 + 8x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + 8x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 8x + x2 = 0 + 200 8x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 8x + x2 = 200 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 = 200 + 16 Reorder the terms: 16 + 8x + x2 = 200 + 16 Combine like terms: 200 + 16 = 216 16 + 8x + x2 = 216 Factor a perfect square on the left side: (x + 4)(x + 4) = 216 Calculate the square root of the right side: 14.696938457 Break this problem into two subproblems by setting (x + 4) equal to 14.696938457 and -14.696938457.Subproblem 1
x + 4 = 14.696938457 Simplifying x + 4 = 14.696938457 Reorder the terms: 4 + x = 14.696938457 Solving 4 + x = 14.696938457 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 = 14.696938457 + -4 Combine like terms: 4 + -4 = 0 0 + x = 14.696938457 + -4 x = 14.696938457 + -4 Combine like terms: 14.696938457 + -4 = 10.696938457 x = 10.696938457 Simplifying x = 10.696938457Subproblem 2
x + 4 = -14.696938457 Simplifying x + 4 = -14.696938457 Reorder the terms: 4 + x = -14.696938457 Solving 4 + x = -14.696938457 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 = -14.696938457 + -4 Combine like terms: 4 + -4 = 0 0 + x = -14.696938457 + -4 x = -14.696938457 + -4 Combine like terms: -14.696938457 + -4 = -18.696938457 x = -18.696938457 Simplifying x = -18.696938457Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.696938457, -18.696938457}Solution
x = {10.696938457, -18.696938457}
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