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Simplifying 28(2x + -1) = 7(x + 3) * 2x Reorder the terms: 28(-1 + 2x) = 7(x + 3) * 2x (-1 * 28 + 2x * 28) = 7(x + 3) * 2x (-28 + 56x) = 7(x + 3) * 2x Reorder the terms: -28 + 56x = 7(3 + x) * 2x Reorder the terms for easier multiplication: -28 + 56x = 7 * 2x(3 + x) Multiply 7 * 2 -28 + 56x = 14x(3 + x) -28 + 56x = (3 * 14x + x * 14x) -28 + 56x = (42x + 14x2) Solving -28 + 56x = 42x + 14x2 Solving for variable 'x'. Combine like terms: 56x + -42x = 14x -28 + 14x + -14x2 = 42x + 14x2 + -42x + -14x2 Reorder the terms: -28 + 14x + -14x2 = 42x + -42x + 14x2 + -14x2 Combine like terms: 42x + -42x = 0 -28 + 14x + -14x2 = 0 + 14x2 + -14x2 -28 + 14x + -14x2 = 14x2 + -14x2 Combine like terms: 14x2 + -14x2 = 0 -28 + 14x + -14x2 = 0 Factor out the Greatest Common Factor (GCF), '14'. 14(-2 + x + -1x2) = 0 Ignore the factor 14.Subproblem 1
Set the factor '(-2 + x + -1x2)' equal to zero and attempt to solve: Simplifying -2 + x + -1x2 = 0 Solving -2 + x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -1x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -1x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -1x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x + x2 = 0 + -2 -1x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1x + x2 = -2 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -2 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -2 + 0.25 Combine like terms: -2 + 0.25 = -1.75 0.25 + -1x + x2 = -1.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -1.75 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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