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Simplifying 20X2 + -182X + -200 = 0 Reorder the terms: -200 + -182X + 20X2 = 0 Solving -200 + -182X + 20X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '2'. 2(-100 + -91X + 10X2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-100 + -91X + 10X2)' equal to zero and attempt to solve: Simplifying -100 + -91X + 10X2 = 0 Solving -100 + -91X + 10X2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -10 + -9.1X + X2 = 0.0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -9.1X + 10 + X2 = 0.0 + 10 Reorder the terms: -10 + 10 + -9.1X + X2 = 0.0 + 10 Combine like terms: -10 + 10 = 0 0 + -9.1X + X2 = 0.0 + 10 -9.1X + X2 = 0.0 + 10 Combine like terms: 0.0 + 10 = 10 -9.1X + X2 = 10 The X term is -9.1X. Take half its coefficient (-4.55). Square it (20.7025) and add it to both sides. Add '20.7025' to each side of the equation. -9.1X + 20.7025 + X2 = 10 + 20.7025 Reorder the terms: 20.7025 + -9.1X + X2 = 10 + 20.7025 Combine like terms: 10 + 20.7025 = 30.7025 20.7025 + -9.1X + X2 = 30.7025 Factor a perfect square on the left side: (X + -4.55)(X + -4.55) = 30.7025 Calculate the square root of the right side: 5.540983667 Break this problem into two subproblems by setting (X + -4.55) equal to 5.540983667 and -5.540983667.Subproblem 1
X + -4.55 = 5.540983667 Simplifying X + -4.55 = 5.540983667 Reorder the terms: -4.55 + X = 5.540983667 Solving -4.55 + X = 5.540983667 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '4.55' to each side of the equation. -4.55 + 4.55 + X = 5.540983667 + 4.55 Combine like terms: -4.55 + 4.55 = 0.00 0.00 + X = 5.540983667 + 4.55 X = 5.540983667 + 4.55 Combine like terms: 5.540983667 + 4.55 = 10.090983667 X = 10.090983667 Simplifying X = 10.090983667Subproblem 2
X + -4.55 = -5.540983667 Simplifying X + -4.55 = -5.540983667 Reorder the terms: -4.55 + X = -5.540983667 Solving -4.55 + X = -5.540983667 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '4.55' to each side of the equation. -4.55 + 4.55 + X = -5.540983667 + 4.55 Combine like terms: -4.55 + 4.55 = 0.00 0.00 + X = -5.540983667 + 4.55 X = -5.540983667 + 4.55 Combine like terms: -5.540983667 + 4.55 = -0.990983667 X = -0.990983667 Simplifying X = -0.990983667Solution
The solution to the problem is based on the solutions from the subproblems. X = {10.090983667, -0.990983667}Solution
X = {10.090983667, -0.990983667}
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