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Simplifying 4(x + -5)(x + -5) + 12 = 0 Reorder the terms: 4(-5 + x)(x + -5) + 12 = 0 Reorder the terms: 4(-5 + x)(-5 + x) + 12 = 0 Multiply (-5 + x) * (-5 + x) 4(-5(-5 + x) + x(-5 + x)) + 12 = 0 4((-5 * -5 + x * -5) + x(-5 + x)) + 12 = 0 4((25 + -5x) + x(-5 + x)) + 12 = 0 4(25 + -5x + (-5 * x + x * x)) + 12 = 0 4(25 + -5x + (-5x + x2)) + 12 = 0 Combine like terms: -5x + -5x = -10x 4(25 + -10x + x2) + 12 = 0 (25 * 4 + -10x * 4 + x2 * 4) + 12 = 0 (100 + -40x + 4x2) + 12 = 0 Reorder the terms: 100 + 12 + -40x + 4x2 = 0 Combine like terms: 100 + 12 = 112 112 + -40x + 4x2 = 0 Solving 112 + -40x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(28 + -10x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(28 + -10x + x2)' equal to zero and attempt to solve: Simplifying 28 + -10x + x2 = 0 Solving 28 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-28' to each side of the equation. 28 + -10x + -28 + x2 = 0 + -28 Reorder the terms: 28 + -28 + -10x + x2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -10x + x2 = 0 + -28 -10x + x2 = 0 + -28 Combine like terms: 0 + -28 = -28 -10x + x2 = -28 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 = -28 + 25 Reorder the terms: 25 + -10x + x2 = -28 + 25 Combine like terms: -28 + 25 = -3 25 + -10x + x2 = -3 Factor a perfect square on the left side: (x + -5)(x + -5) = -3 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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