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Simplifying 10 + -1X + 2X(-10X) = 310 Remove parenthesis around (-10X) 10 + -1X + 2X * -10X = 310 Reorder the terms for easier multiplication: 10 + -1X + 2 * -10X * X = 310 Multiply 2 * -10 10 + -1X + -20X * X = 310 Multiply X * X 10 + -1X + -20X2 = 310 Solving 10 + -1X + -20X2 = 310 Solving for variable 'X'. Reorder the terms: 10 + -310 + -1X + -20X2 = 310 + -310 Combine like terms: 10 + -310 = -300 -300 + -1X + -20X2 = 310 + -310 Combine like terms: 310 + -310 = 0 -300 + -1X + -20X2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(300 + X + 20X2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(300 + X + 20X2)' equal to zero and attempt to solve: Simplifying 300 + X + 20X2 = 0 Solving 300 + X + 20X2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 15 + 0.05X + X2 = 0.0 Move the constant term to the right: Add '-15' to each side of the equation. 15 + 0.05X + -15 + X2 = 0.0 + -15 Reorder the terms: 15 + -15 + 0.05X + X2 = 0.0 + -15 Combine like terms: 15 + -15 = 0 0 + 0.05X + X2 = 0.0 + -15 0.05X + X2 = 0.0 + -15 Combine like terms: 0.0 + -15 = -15 0.05X + X2 = -15 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. 0.05X + 0.25 + X2 = -15 + 0.25 Reorder the terms: 0.25 + 0.05X + X2 = -15 + 0.25 Combine like terms: -15 + 0.25 = -14.75 0.25 + 0.05X + X2 = -14.75 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = -14.75 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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