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Simplifying 4x2 + -32 = -24x Reorder the terms: -32 + 4x2 = -24x Solving -32 + 4x2 = -24x Solving for variable 'x'. Reorder the terms: -32 + 24x + 4x2 = -24x + 24x Combine like terms: -24x + 24x = 0 -32 + 24x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-8 + 6x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-8 + 6x + x2)' equal to zero and attempt to solve: Simplifying -8 + 6x + x2 = 0 Solving -8 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 6x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 6x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 6x + x2 = 0 + 8 6x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 6x + x2 = 8 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 = 8 + 9 Reorder the terms: 9 + 6x + x2 = 8 + 9 Combine like terms: 8 + 9 = 17 9 + 6x + x2 = 17 Factor a perfect square on the left side: (x + 3)(x + 3) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (x + 3) equal to 4.123105626 and -4.123105626.Subproblem 1
x + 3 = 4.123105626 Simplifying x + 3 = 4.123105626 Reorder the terms: 3 + x = 4.123105626 Solving 3 + x = 4.123105626 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 = 4.123105626 + -3 Combine like terms: 3 + -3 = 0 0 + x = 4.123105626 + -3 x = 4.123105626 + -3 Combine like terms: 4.123105626 + -3 = 1.123105626 x = 1.123105626 Simplifying x = 1.123105626Subproblem 2
x + 3 = -4.123105626 Simplifying x + 3 = -4.123105626 Reorder the terms: 3 + x = -4.123105626 Solving 3 + x = -4.123105626 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 = -4.123105626 + -3 Combine like terms: 3 + -3 = 0 0 + x = -4.123105626 + -3 x = -4.123105626 + -3 Combine like terms: -4.123105626 + -3 = -7.123105626 x = -7.123105626 Simplifying x = -7.123105626Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.123105626, -7.123105626}Solution
x = {1.123105626, -7.123105626}
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