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Simplifying 0 = x2 + 7x + 32 Reorder the terms: 0 = 32 + 7x + x2 Solving 0 = 32 + 7x + x2 Solving for variable 'x'. Combine like terms: 0 + -32 = -32 -32 + -7x + -1x2 = 32 + 7x + x2 + -32 + -7x + -1x2 Reorder the terms: -32 + -7x + -1x2 = 32 + -32 + 7x + -7x + x2 + -1x2 Combine like terms: 32 + -32 = 0 -32 + -7x + -1x2 = 0 + 7x + -7x + x2 + -1x2 -32 + -7x + -1x2 = 7x + -7x + x2 + -1x2 Combine like terms: 7x + -7x = 0 -32 + -7x + -1x2 = 0 + x2 + -1x2 -32 + -7x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -32 + -7x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(32 + 7x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(32 + 7x + x2)' equal to zero and attempt to solve: Simplifying 32 + 7x + x2 = 0 Solving 32 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + 7x + -32 + x2 = 0 + -32 Reorder the terms: 32 + -32 + 7x + x2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + 7x + x2 = 0 + -32 7x + x2 = 0 + -32 Combine like terms: 0 + -32 = -32 7x + x2 = -32 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -32 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -32 + 12.25 Combine like terms: -32 + 12.25 = -19.75 12.25 + 7x + x2 = -19.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = -19.75 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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