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Simplifying -16x2 + 64x + 200 = 0 Reorder the terms: 200 + 64x + -16x2 = 0 Solving 200 + 64x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(25 + 8x + -2x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(25 + 8x + -2x2)' equal to zero and attempt to solve: Simplifying 25 + 8x + -2x2 = 0 Solving 25 + 8x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -12.5 + -4x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -4x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -4x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -4x + x2 = 0 + 12.5 -4x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -4x + x2 = 12.5 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 = 12.5 + 4 Reorder the terms: 4 + -4x + x2 = 12.5 + 4 Combine like terms: 12.5 + 4 = 16.5 4 + -4x + x2 = 16.5 Factor a perfect square on the left side: (x + -2)(x + -2) = 16.5 Calculate the square root of the right side: 4.062019202 Break this problem into two subproblems by setting (x + -2) equal to 4.062019202 and -4.062019202.Subproblem 1
x + -2 = 4.062019202 Simplifying x + -2 = 4.062019202 Reorder the terms: -2 + x = 4.062019202 Solving -2 + x = 4.062019202 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 = 4.062019202 + 2 Combine like terms: -2 + 2 = 0 0 + x = 4.062019202 + 2 x = 4.062019202 + 2 Combine like terms: 4.062019202 + 2 = 6.062019202 x = 6.062019202 Simplifying x = 6.062019202Subproblem 2
x + -2 = -4.062019202 Simplifying x + -2 = -4.062019202 Reorder the terms: -2 + x = -4.062019202 Solving -2 + x = -4.062019202 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 = -4.062019202 + 2 Combine like terms: -2 + 2 = 0 0 + x = -4.062019202 + 2 x = -4.062019202 + 2 Combine like terms: -4.062019202 + 2 = -2.062019202 x = -2.062019202 Simplifying x = -2.062019202Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.062019202, -2.062019202}Solution
x = {6.062019202, -2.062019202}
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