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Simplifying 25x2 + -9x + -180 = 0 Reorder the terms: -180 + -9x + 25x2 = 0 Solving -180 + -9x + 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'. -7.2 + -0.36x + x2 = 0 Move the constant term to the right: Add '7.2' to each side of the equation. -7.2 + -0.36x + 7.2 + x2 = 0 + 7.2 Reorder the terms: -7.2 + 7.2 + -0.36x + x2 = 0 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + -0.36x + x2 = 0 + 7.2 -0.36x + x2 = 0 + 7.2 Combine like terms: 0 + 7.2 = 7.2 -0.36x + x2 = 7.2 The x term is -0.36x. Take half its coefficient (-0.18). Square it (0.0324) and add it to both sides. Add '0.0324' to each side of the equation. -0.36x + 0.0324 + x2 = 7.2 + 0.0324 Reorder the terms: 0.0324 + -0.36x + x2 = 7.2 + 0.0324 Combine like terms: 7.2 + 0.0324 = 7.2324 0.0324 + -0.36x + x2 = 7.2324 Factor a perfect square on the left side: (x + -0.18)(x + -0.18) = 7.2324 Calculate the square root of the right side: 2.68931218 Break this problem into two subproblems by setting (x + -0.18) equal to 2.68931218 and -2.68931218.Subproblem 1
x + -0.18 = 2.68931218 Simplifying x + -0.18 = 2.68931218 Reorder the terms: -0.18 + x = 2.68931218 Solving -0.18 + x = 2.68931218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.18' to each side of the equation. -0.18 + 0.18 + x = 2.68931218 + 0.18 Combine like terms: -0.18 + 0.18 = 0.00 0.00 + x = 2.68931218 + 0.18 x = 2.68931218 + 0.18 Combine like terms: 2.68931218 + 0.18 = 2.86931218 x = 2.86931218 Simplifying x = 2.86931218Subproblem 2
x + -0.18 = -2.68931218 Simplifying x + -0.18 = -2.68931218 Reorder the terms: -0.18 + x = -2.68931218 Solving -0.18 + x = -2.68931218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.18' to each side of the equation. -0.18 + 0.18 + x = -2.68931218 + 0.18 Combine like terms: -0.18 + 0.18 = 0.00 0.00 + x = -2.68931218 + 0.18 x = -2.68931218 + 0.18 Combine like terms: -2.68931218 + 0.18 = -2.50931218 x = -2.50931218 Simplifying x = -2.50931218Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.86931218, -2.50931218}
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