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Simplifying 4x2 + 76 = 16x Reorder the terms: 76 + 4x2 = 16x Solving 76 + 4x2 = 16x Solving for variable 'x'. Reorder the terms: 76 + -16x + 4x2 = 16x + -16x Combine like terms: 16x + -16x = 0 76 + -16x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(19 + -4x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(19 + -4x + x2)' equal to zero and attempt to solve: Simplifying 19 + -4x + x2 = 0 Solving 19 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + -4x + -19 + x2 = 0 + -19 Reorder the terms: 19 + -19 + -4x + x2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -4x + x2 = 0 + -19 -4x + x2 = 0 + -19 Combine like terms: 0 + -19 = -19 -4x + x2 = -19 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -19 + 4 Reorder the terms: 4 + -4x + x2 = -19 + 4 Combine like terms: -19 + 4 = -15 4 + -4x + x2 = -15 Factor a perfect square on the left side: (x + -2)(x + -2) = -15 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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