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Simplifying 90 + -1x * 5x + 10x = 500 Reorder the terms for easier multiplication: 90 + -1 * 5x * x + 10x = 500 Multiply -1 * 5 90 + -5x * x + 10x = 500 Multiply x * x 90 + -5x2 + 10x = 500 Reorder the terms: 90 + 10x + -5x2 = 500 Solving 90 + 10x + -5x2 = 500 Solving for variable 'x'. Reorder the terms: 90 + -500 + 10x + -5x2 = 500 + -500 Combine like terms: 90 + -500 = -410 -410 + 10x + -5x2 = 500 + -500 Combine like terms: 500 + -500 = 0 -410 + 10x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-82 + 2x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-82 + 2x + -1x2)' equal to zero and attempt to solve: Simplifying -82 + 2x + -1x2 = 0 Solving -82 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 82 + -2x + x2 = 0 Move the constant term to the right: Add '-82' to each side of the equation. 82 + -2x + -82 + x2 = 0 + -82 Reorder the terms: 82 + -82 + -2x + x2 = 0 + -82 Combine like terms: 82 + -82 = 0 0 + -2x + x2 = 0 + -82 -2x + x2 = 0 + -82 Combine like terms: 0 + -82 = -82 -2x + x2 = -82 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 = -82 + 1 Reorder the terms: 1 + -2x + x2 = -82 + 1 Combine like terms: -82 + 1 = -81 1 + -2x + x2 = -81 Factor a perfect square on the left side: (x + -1)(x + -1) = -81 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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