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Simplifying 4x2 + -32x + -17 = 25 Reorder the terms: -17 + -32x + 4x2 = 25 Solving -17 + -32x + 4x2 = 25 Solving for variable 'x'. Reorder the terms: -17 + -25 + -32x + 4x2 = 25 + -25 Combine like terms: -17 + -25 = -42 -42 + -32x + 4x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -42 + -32x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + -16x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-21 + -16x + 2x2)' equal to zero and attempt to solve: Simplifying -21 + -16x + 2x2 = 0 Solving -21 + -16x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10.5 + -8x + x2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + -8x + 10.5 + x2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + -8x + x2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + -8x + x2 = 0 + 10.5 -8x + x2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 -8x + x2 = 10.5 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 = 10.5 + 16 Reorder the terms: 16 + -8x + x2 = 10.5 + 16 Combine like terms: 10.5 + 16 = 26.5 16 + -8x + x2 = 26.5 Factor a perfect square on the left side: (x + -4)(x + -4) = 26.5 Calculate the square root of the right side: 5.14781507 Break this problem into two subproblems by setting (x + -4) equal to 5.14781507 and -5.14781507.Subproblem 1
x + -4 = 5.14781507 Simplifying x + -4 = 5.14781507 Reorder the terms: -4 + x = 5.14781507 Solving -4 + x = 5.14781507 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 = 5.14781507 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.14781507 + 4 x = 5.14781507 + 4 Combine like terms: 5.14781507 + 4 = 9.14781507 x = 9.14781507 Simplifying x = 9.14781507Subproblem 2
x + -4 = -5.14781507 Simplifying x + -4 = -5.14781507 Reorder the terms: -4 + x = -5.14781507 Solving -4 + x = -5.14781507 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 = -5.14781507 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.14781507 + 4 x = -5.14781507 + 4 Combine like terms: -5.14781507 + 4 = -1.14781507 x = -1.14781507 Simplifying x = -1.14781507Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.14781507, -1.14781507}Solution
x = {9.14781507, -1.14781507}
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