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Simplifying 10X2 + 2X + -90 = 0 Reorder the terms: -90 + 2X + 10X2 = 0 Solving -90 + 2X + 10X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '2'. 2(-45 + X + 5X2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-45 + X + 5X2)' equal to zero and attempt to solve: Simplifying -45 + X + 5X2 = 0 Solving -45 + X + 5X2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -9 + 0.2X + X2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 0.2X + 9 + X2 = 0 + 9 Reorder the terms: -9 + 9 + 0.2X + X2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 0.2X + X2 = 0 + 9 0.2X + X2 = 0 + 9 Combine like terms: 0 + 9 = 9 0.2X + X2 = 9 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. 0.2X + 0.25 + X2 = 9 + 0.25 Reorder the terms: 0.25 + 0.2X + X2 = 9 + 0.25 Combine like terms: 9 + 0.25 = 9.25 0.25 + 0.2X + X2 = 9.25 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (X + 0.5) equal to 3.041381265 and -3.041381265.Subproblem 1
X + 0.5 = 3.041381265 Simplifying X + 0.5 = 3.041381265 Reorder the terms: 0.5 + X = 3.041381265 Solving 0.5 + X = 3.041381265 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = 3.041381265 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 3.041381265 + -0.5 X = 3.041381265 + -0.5 Combine like terms: 3.041381265 + -0.5 = 2.541381265 X = 2.541381265 Simplifying X = 2.541381265Subproblem 2
X + 0.5 = -3.041381265 Simplifying X + 0.5 = -3.041381265 Reorder the terms: 0.5 + X = -3.041381265 Solving 0.5 + X = -3.041381265 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = -3.041381265 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -3.041381265 + -0.5 X = -3.041381265 + -0.5 Combine like terms: -3.041381265 + -0.5 = -3.541381265 X = -3.541381265 Simplifying X = -3.541381265Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.541381265, -3.541381265}Solution
X = {2.541381265, -3.541381265}
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