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Simplifying 0 = -16x2 + 32x + 100 Reorder the terms: 0 = 100 + 32x + -16x2 Solving 0 = 100 + 32x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -100 = -100 -100 + -32x + 16x2 = 100 + 32x + -16x2 + -100 + -32x + 16x2 Reorder the terms: -100 + -32x + 16x2 = 100 + -100 + 32x + -32x + -16x2 + 16x2 Combine like terms: 100 + -100 = 0 -100 + -32x + 16x2 = 0 + 32x + -32x + -16x2 + 16x2 -100 + -32x + 16x2 = 32x + -32x + -16x2 + 16x2 Combine like terms: 32x + -32x = 0 -100 + -32x + 16x2 = 0 + -16x2 + 16x2 -100 + -32x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -100 + -32x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-25 + -8x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-25 + -8x + 4x2)' equal to zero and attempt to solve: Simplifying -25 + -8x + 4x2 = 0 Solving -25 + -8x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.25 + -2x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -2x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -2x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -2x + x2 = 0 + 6.25 -2x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -2x + x2 = 6.25 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 = 6.25 + 1 Reorder the terms: 1 + -2x + x2 = 6.25 + 1 Combine like terms: 6.25 + 1 = 7.25 1 + -2x + x2 = 7.25 Factor a perfect square on the left side: (x + -1)(x + -1) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (x + -1) equal to 2.692582404 and -2.692582404.Subproblem 1
x + -1 = 2.692582404 Simplifying x + -1 = 2.692582404 Reorder the terms: -1 + x = 2.692582404 Solving -1 + x = 2.692582404 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 = 2.692582404 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.692582404 + 1 x = 2.692582404 + 1 Combine like terms: 2.692582404 + 1 = 3.692582404 x = 3.692582404 Simplifying x = 3.692582404Subproblem 2
x + -1 = -2.692582404 Simplifying x + -1 = -2.692582404 Reorder the terms: -1 + x = -2.692582404 Solving -1 + x = -2.692582404 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 = -2.692582404 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.692582404 + 1 x = -2.692582404 + 1 Combine like terms: -2.692582404 + 1 = -1.692582404 x = -1.692582404 Simplifying x = -1.692582404Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.692582404, -1.692582404}Solution
x = {3.692582404, -1.692582404}
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