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Simplifying 7(x) = 2x + x2 + 3(4x) + 17 Remove parenthesis around (4x) 7x = 2x + x2 + 3 * 4x + 17 Multiply 3 * 4 7x = 2x + x2 + 12x + 17 Reorder the terms: 7x = 17 + 2x + 12x + x2 Combine like terms: 2x + 12x = 14x 7x = 17 + 14x + x2 Solving 7x = 17 + 14x + x2 Solving for variable 'x'. Reorder the terms: -17 + 7x + -14x + -1x2 = 17 + 14x + x2 + -17 + -14x + -1x2 Combine like terms: 7x + -14x = -7x -17 + -7x + -1x2 = 17 + 14x + x2 + -17 + -14x + -1x2 Reorder the terms: -17 + -7x + -1x2 = 17 + -17 + 14x + -14x + x2 + -1x2 Combine like terms: 17 + -17 = 0 -17 + -7x + -1x2 = 0 + 14x + -14x + x2 + -1x2 -17 + -7x + -1x2 = 14x + -14x + x2 + -1x2 Combine like terms: 14x + -14x = 0 -17 + -7x + -1x2 = 0 + x2 + -1x2 -17 + -7x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -17 + -7x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(17 + 7x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(17 + 7x + x2)' equal to zero and attempt to solve: Simplifying 17 + 7x + x2 = 0 Solving 17 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + 7x + -17 + x2 = 0 + -17 Reorder the terms: 17 + -17 + 7x + x2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 7x + x2 = 0 + -17 7x + x2 = 0 + -17 Combine like terms: 0 + -17 = -17 7x + x2 = -17 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 = -17 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -17 + 12.25 Combine like terms: -17 + 12.25 = -4.75 12.25 + 7x + x2 = -4.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = -4.75 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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