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Simplifying 0 = x2 + 10x + 50 Reorder the terms: 0 = 50 + 10x + x2 Solving 0 = 50 + 10x + x2 Solving for variable 'x'. Combine like terms: 0 + -50 = -50 -50 + -10x + -1x2 = 50 + 10x + x2 + -50 + -10x + -1x2 Reorder the terms: -50 + -10x + -1x2 = 50 + -50 + 10x + -10x + x2 + -1x2 Combine like terms: 50 + -50 = 0 -50 + -10x + -1x2 = 0 + 10x + -10x + x2 + -1x2 -50 + -10x + -1x2 = 10x + -10x + x2 + -1x2 Combine like terms: 10x + -10x = 0 -50 + -10x + -1x2 = 0 + x2 + -1x2 -50 + -10x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -50 + -10x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(50 + 10x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(50 + 10x + x2)' equal to zero and attempt to solve: Simplifying 50 + 10x + x2 = 0 Solving 50 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-50' to each side of the equation. 50 + 10x + -50 + x2 = 0 + -50 Reorder the terms: 50 + -50 + 10x + x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + 10x + x2 = 0 + -50 10x + x2 = 0 + -50 Combine like terms: 0 + -50 = -50 10x + x2 = -50 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -50 + 25 Reorder the terms: 25 + 10x + x2 = -50 + 25 Combine like terms: -50 + 25 = -25 25 + 10x + x2 = -25 Factor a perfect square on the left side: (x + 5)(x + 5) = -25 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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