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Simplifying -5x2 = 10 + -10x Solving -5x2 = 10 + -10x Solving for variable 'x'. Reorder the terms: -10 + 10x + -5x2 = 10 + -10x + -10 + 10x Reorder the terms: -10 + 10x + -5x2 = 10 + -10 + -10x + 10x Combine like terms: 10 + -10 = 0 -10 + 10x + -5x2 = 0 + -10x + 10x -10 + 10x + -5x2 = -10x + 10x Combine like terms: -10x + 10x = 0 -10 + 10x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-2 + 2x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-2 + 2x + -1x2)' equal to zero and attempt to solve: Simplifying -2 + 2x + -1x2 = 0 Solving -2 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -2x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -2x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -2x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2x + x2 = 0 + -2 -2x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -2x + x2 = -2 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 = -2 + 1 Reorder the terms: 1 + -2x + x2 = -2 + 1 Combine like terms: -2 + 1 = -1 1 + -2x + x2 = -1 Factor a perfect square on the left side: (x + -1)(x + -1) = -1 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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