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Simplifying 25X2 + -10X + -90 = 0 Reorder the terms: -90 + -10X + 25X2 = 0 Solving -90 + -10X + 25X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '5'. 5(-18 + -2X + 5X2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-18 + -2X + 5X2)' equal to zero and attempt to solve: Simplifying -18 + -2X + 5X2 = 0 Solving -18 + -2X + 5X2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.6 + -0.4X + X2 = 0 Move the constant term to the right: Add '3.6' to each side of the equation. -3.6 + -0.4X + 3.6 + X2 = 0 + 3.6 Reorder the terms: -3.6 + 3.6 + -0.4X + X2 = 0 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + -0.4X + X2 = 0 + 3.6 -0.4X + X2 = 0 + 3.6 Combine like terms: 0 + 3.6 = 3.6 -0.4X + X2 = 3.6 The X term is -0.4X. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4X + 0.04 + X2 = 3.6 + 0.04 Reorder the terms: 0.04 + -0.4X + X2 = 3.6 + 0.04 Combine like terms: 3.6 + 0.04 = 3.64 0.04 + -0.4X + X2 = 3.64 Factor a perfect square on the left side: (X + -0.2)(X + -0.2) = 3.64 Calculate the square root of the right side: 1.907878403 Break this problem into two subproblems by setting (X + -0.2) equal to 1.907878403 and -1.907878403.Subproblem 1
X + -0.2 = 1.907878403 Simplifying X + -0.2 = 1.907878403 Reorder the terms: -0.2 + X = 1.907878403 Solving -0.2 + X = 1.907878403 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + X = 1.907878403 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + X = 1.907878403 + 0.2 X = 1.907878403 + 0.2 Combine like terms: 1.907878403 + 0.2 = 2.107878403 X = 2.107878403 Simplifying X = 2.107878403Subproblem 2
X + -0.2 = -1.907878403 Simplifying X + -0.2 = -1.907878403 Reorder the terms: -0.2 + X = -1.907878403 Solving -0.2 + X = -1.907878403 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + X = -1.907878403 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + X = -1.907878403 + 0.2 X = -1.907878403 + 0.2 Combine like terms: -1.907878403 + 0.2 = -1.707878403 X = -1.707878403 Simplifying X = -1.707878403Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.107878403, -1.707878403}Solution
X = {2.107878403, -1.707878403}
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