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Simplifying 10 = 2x2 + -16x + -32 Reorder the terms: 10 = -32 + -16x + 2x2 Solving 10 = -32 + -16x + 2x2 Solving for variable 'x'. Combine like terms: 10 + 32 = 42 42 + 16x + -2x2 = -32 + -16x + 2x2 + 32 + 16x + -2x2 Reorder the terms: 42 + 16x + -2x2 = -32 + 32 + -16x + 16x + 2x2 + -2x2 Combine like terms: -32 + 32 = 0 42 + 16x + -2x2 = 0 + -16x + 16x + 2x2 + -2x2 42 + 16x + -2x2 = -16x + 16x + 2x2 + -2x2 Combine like terms: -16x + 16x = 0 42 + 16x + -2x2 = 0 + 2x2 + -2x2 42 + 16x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 42 + 16x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(21 + 8x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(21 + 8x + -1x2)' equal to zero and attempt to solve: Simplifying 21 + 8x + -1x2 = 0 Solving 21 + 8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -21 + -8x + x2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + -8x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + -8x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -8x + x2 = 0 + 21 -8x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 -8x + x2 = 21 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 = 21 + 16 Reorder the terms: 16 + -8x + x2 = 21 + 16 Combine like terms: 21 + 16 = 37 16 + -8x + x2 = 37 Factor a perfect square on the left side: (x + -4)(x + -4) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (x + -4) equal to 6.08276253 and -6.08276253.Subproblem 1
x + -4 = 6.08276253 Simplifying x + -4 = 6.08276253 Reorder the terms: -4 + x = 6.08276253 Solving -4 + x = 6.08276253 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 = 6.08276253 + 4 Combine like terms: -4 + 4 = 0 0 + x = 6.08276253 + 4 x = 6.08276253 + 4 Combine like terms: 6.08276253 + 4 = 10.08276253 x = 10.08276253 Simplifying x = 10.08276253Subproblem 2
x + -4 = -6.08276253 Simplifying x + -4 = -6.08276253 Reorder the terms: -4 + x = -6.08276253 Solving -4 + x = -6.08276253 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 = -6.08276253 + 4 Combine like terms: -4 + 4 = 0 0 + x = -6.08276253 + 4 x = -6.08276253 + 4 Combine like terms: -6.08276253 + 4 = -2.08276253 x = -2.08276253 Simplifying x = -2.08276253Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.08276253, -2.08276253}Solution
x = {10.08276253, -2.08276253}
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