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Simplifying 25x2 + -6x + -30 = 0 Reorder the terms: -30 + -6x + 25x2 = 0 Solving -30 + -6x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -1.2 + -0.24x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -0.24x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -0.24x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -0.24x + x2 = 0 + 1.2 -0.24x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -0.24x + x2 = 1.2 The x term is -0.24x. Take half its coefficient (-0.12). Square it (0.0144) and add it to both sides. Add '0.0144' to each side of the equation. -0.24x + 0.0144 + x2 = 1.2 + 0.0144 Reorder the terms: 0.0144 + -0.24x + x2 = 1.2 + 0.0144 Combine like terms: 1.2 + 0.0144 = 1.2144 0.0144 + -0.24x + x2 = 1.2144 Factor a perfect square on the left side: (x + -0.12)(x + -0.12) = 1.2144 Calculate the square root of the right side: 1.101998185 Break this problem into two subproblems by setting (x + -0.12) equal to 1.101998185 and -1.101998185.Subproblem 1
x + -0.12 = 1.101998185 Simplifying x + -0.12 = 1.101998185 Reorder the terms: -0.12 + x = 1.101998185 Solving -0.12 + x = 1.101998185 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.12' to each side of the equation. -0.12 + 0.12 + x = 1.101998185 + 0.12 Combine like terms: -0.12 + 0.12 = 0.00 0.00 + x = 1.101998185 + 0.12 x = 1.101998185 + 0.12 Combine like terms: 1.101998185 + 0.12 = 1.221998185 x = 1.221998185 Simplifying x = 1.221998185Subproblem 2
x + -0.12 = -1.101998185 Simplifying x + -0.12 = -1.101998185 Reorder the terms: -0.12 + x = -1.101998185 Solving -0.12 + x = -1.101998185 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.12' to each side of the equation. -0.12 + 0.12 + x = -1.101998185 + 0.12 Combine like terms: -0.12 + 0.12 = 0.00 0.00 + x = -1.101998185 + 0.12 x = -1.101998185 + 0.12 Combine like terms: -1.101998185 + 0.12 = -0.981998185 x = -0.981998185 Simplifying x = -0.981998185Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.221998185, -0.981998185}
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