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Simplifying 2(x + -5)(x + -5) + 10 = 0 Reorder the terms: 2(-5 + x)(x + -5) + 10 = 0 Reorder the terms: 2(-5 + x)(-5 + x) + 10 = 0 Multiply (-5 + x) * (-5 + x) 2(-5(-5 + x) + x(-5 + x)) + 10 = 0 2((-5 * -5 + x * -5) + x(-5 + x)) + 10 = 0 2((25 + -5x) + x(-5 + x)) + 10 = 0 2(25 + -5x + (-5 * x + x * x)) + 10 = 0 2(25 + -5x + (-5x + x2)) + 10 = 0 Combine like terms: -5x + -5x = -10x 2(25 + -10x + x2) + 10 = 0 (25 * 2 + -10x * 2 + x2 * 2) + 10 = 0 (50 + -20x + 2x2) + 10 = 0 Reorder the terms: 50 + 10 + -20x + 2x2 = 0 Combine like terms: 50 + 10 = 60 60 + -20x + 2x2 = 0 Solving 60 + -20x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(30 + -10x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(30 + -10x + x2)' equal to zero and attempt to solve: Simplifying 30 + -10x + x2 = 0 Solving 30 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + -10x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + -10x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -10x + x2 = 0 + -30 -10x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 -10x + x2 = -30 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 = -30 + 25 Reorder the terms: 25 + -10x + x2 = -30 + 25 Combine like terms: -30 + 25 = -5 25 + -10x + x2 = -5 Factor a perfect square on the left side: (x + -5)(x + -5) = -5 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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