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Simplifying 10X2 + -2X + -115 = 0 Reorder the terms: -115 + -2X + 10X2 = 0 Solving -115 + -2X + 10X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -11.5 + -0.2X + X2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + -0.2X + 11.5 + X2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + -0.2X + X2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + -0.2X + X2 = 0 + 11.5 -0.2X + X2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 -0.2X + X2 = 11.5 The X term is -0.2X. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2X + 0.01 + X2 = 11.5 + 0.01 Reorder the terms: 0.01 + -0.2X + X2 = 11.5 + 0.01 Combine like terms: 11.5 + 0.01 = 11.51 0.01 + -0.2X + X2 = 11.51 Factor a perfect square on the left side: (X + -0.1)(X + -0.1) = 11.51 Calculate the square root of the right side: 3.392639091 Break this problem into two subproblems by setting (X + -0.1) equal to 3.392639091 and -3.392639091.Subproblem 1
X + -0.1 = 3.392639091 Simplifying X + -0.1 = 3.392639091 Reorder the terms: -0.1 + X = 3.392639091 Solving -0.1 + X = 3.392639091 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + X = 3.392639091 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + X = 3.392639091 + 0.1 X = 3.392639091 + 0.1 Combine like terms: 3.392639091 + 0.1 = 3.492639091 X = 3.492639091 Simplifying X = 3.492639091Subproblem 2
X + -0.1 = -3.392639091 Simplifying X + -0.1 = -3.392639091 Reorder the terms: -0.1 + X = -3.392639091 Solving -0.1 + X = -3.392639091 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + X = -3.392639091 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + X = -3.392639091 + 0.1 X = -3.392639091 + 0.1 Combine like terms: -3.392639091 + 0.1 = -3.292639091 X = -3.292639091 Simplifying X = -3.292639091Solution
The solution to the problem is based on the solutions from the subproblems. X = {3.492639091, -3.292639091}
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