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Simplifying 209 = 16x2 + -32x + -15 Reorder the terms: 209 = -15 + -32x + 16x2 Solving 209 = -15 + -32x + 16x2 Solving for variable 'x'. Combine like terms: 209 + 15 = 224 224 + 32x + -16x2 = -15 + -32x + 16x2 + 15 + 32x + -16x2 Reorder the terms: 224 + 32x + -16x2 = -15 + 15 + -32x + 32x + 16x2 + -16x2 Combine like terms: -15 + 15 = 0 224 + 32x + -16x2 = 0 + -32x + 32x + 16x2 + -16x2 224 + 32x + -16x2 = -32x + 32x + 16x2 + -16x2 Combine like terms: -32x + 32x = 0 224 + 32x + -16x2 = 0 + 16x2 + -16x2 224 + 32x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 224 + 32x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(14 + 2x + -1x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(14 + 2x + -1x2)' equal to zero and attempt to solve: Simplifying 14 + 2x + -1x2 = 0 Solving 14 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -14 + -2x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + -2x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + -2x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -2x + x2 = 0 + 14 -2x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 -2x + x2 = 14 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 = 14 + 1 Reorder the terms: 1 + -2x + x2 = 14 + 1 Combine like terms: 14 + 1 = 15 1 + -2x + x2 = 15 Factor a perfect square on the left side: (x + -1)(x + -1) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x + -1) equal to 3.872983346 and -3.872983346.Subproblem 1
x + -1 = 3.872983346 Simplifying x + -1 = 3.872983346 Reorder the terms: -1 + x = 3.872983346 Solving -1 + x = 3.872983346 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 = 3.872983346 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.872983346 + 1 x = 3.872983346 + 1 Combine like terms: 3.872983346 + 1 = 4.872983346 x = 4.872983346 Simplifying x = 4.872983346Subproblem 2
x + -1 = -3.872983346 Simplifying x + -1 = -3.872983346 Reorder the terms: -1 + x = -3.872983346 Solving -1 + x = -3.872983346 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 = -3.872983346 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.872983346 + 1 x = -3.872983346 + 1 Combine like terms: -3.872983346 + 1 = -2.872983346 x = -2.872983346 Simplifying x = -2.872983346Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.872983346, -2.872983346}Solution
x = {4.872983346, -2.872983346}
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