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Simplifying 32 = 8x2 + -48x Reorder the terms: 32 = -48x + 8x2 Solving 32 = -48x + 8x2 Solving for variable 'x'. Reorder the terms: 32 + 48x + -8x2 = -48x + 48x + 8x2 + -8x2 Combine like terms: -48x + 48x = 0 32 + 48x + -8x2 = 0 + 8x2 + -8x2 32 + 48x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 32 + 48x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(4 + 6x + -1x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(4 + 6x + -1x2)' equal to zero and attempt to solve: Simplifying 4 + 6x + -1x2 = 0 Solving 4 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + -6x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -6x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -6x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -6x + x2 = 0 + 4 -6x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -6x + x2 = 4 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 4 + 9 Reorder the terms: 9 + -6x + x2 = 4 + 9 Combine like terms: 4 + 9 = 13 9 + -6x + x2 = 13 Factor a perfect square on the left side: (x + -3)(x + -3) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (x + -3) equal to 3.605551275 and -3.605551275.Subproblem 1
x + -3 = 3.605551275 Simplifying x + -3 = 3.605551275 Reorder the terms: -3 + x = 3.605551275 Solving -3 + x = 3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.605551275 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.605551275 + 3 x = 3.605551275 + 3 Combine like terms: 3.605551275 + 3 = 6.605551275 x = 6.605551275 Simplifying x = 6.605551275Subproblem 2
x + -3 = -3.605551275 Simplifying x + -3 = -3.605551275 Reorder the terms: -3 + x = -3.605551275 Solving -3 + x = -3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.605551275 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.605551275 + 3 x = -3.605551275 + 3 Combine like terms: -3.605551275 + 3 = -0.605551275 x = -0.605551275 Simplifying x = -0.605551275Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.605551275, -0.605551275}Solution
x = {6.605551275, -0.605551275}
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