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Simplifying 0 = 7x2 + -14x + 49 Reorder the terms: 0 = 49 + -14x + 7x2 Solving 0 = 49 + -14x + 7x2 Solving for variable 'x'. Combine like terms: 0 + -49 = -49 -49 + 14x + -7x2 = 49 + -14x + 7x2 + -49 + 14x + -7x2 Reorder the terms: -49 + 14x + -7x2 = 49 + -49 + -14x + 14x + 7x2 + -7x2 Combine like terms: 49 + -49 = 0 -49 + 14x + -7x2 = 0 + -14x + 14x + 7x2 + -7x2 -49 + 14x + -7x2 = -14x + 14x + 7x2 + -7x2 Combine like terms: -14x + 14x = 0 -49 + 14x + -7x2 = 0 + 7x2 + -7x2 -49 + 14x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 -49 + 14x + -7x2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-7 + 2x + -1x2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-7 + 2x + -1x2)' equal to zero and attempt to solve: Simplifying -7 + 2x + -1x2 = 0 Solving -7 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 7 + -2x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -2x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -2x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2x + x2 = 0 + -7 -2x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -2x + x2 = -7 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -7 + 1 Reorder the terms: 1 + -2x + x2 = -7 + 1 Combine like terms: -7 + 1 = -6 1 + -2x + x2 = -6 Factor a perfect square on the left side: (x + -1)(x + -1) = -6 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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