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Simplifying 25x2 + 102x + -36 = 0 Reorder the terms: -36 + 102x + 25x2 = 0 Solving -36 + 102x + 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'. -1.44 + 4.08x + x2 = 0 Move the constant term to the right: Add '1.44' to each side of the equation. -1.44 + 4.08x + 1.44 + x2 = 0 + 1.44 Reorder the terms: -1.44 + 1.44 + 4.08x + x2 = 0 + 1.44 Combine like terms: -1.44 + 1.44 = 0.00 0.00 + 4.08x + x2 = 0 + 1.44 4.08x + x2 = 0 + 1.44 Combine like terms: 0 + 1.44 = 1.44 4.08x + x2 = 1.44 The x term is 4.08x. Take half its coefficient (2.04). Square it (4.1616) and add it to both sides. Add '4.1616' to each side of the equation. 4.08x + 4.1616 + x2 = 1.44 + 4.1616 Reorder the terms: 4.1616 + 4.08x + x2 = 1.44 + 4.1616 Combine like terms: 1.44 + 4.1616 = 5.6016 4.1616 + 4.08x + x2 = 5.6016 Factor a perfect square on the left side: (x + 2.04)(x + 2.04) = 5.6016 Calculate the square root of the right side: 2.366769951 Break this problem into two subproblems by setting (x + 2.04) equal to 2.366769951 and -2.366769951.Subproblem 1
x + 2.04 = 2.366769951 Simplifying x + 2.04 = 2.366769951 Reorder the terms: 2.04 + x = 2.366769951 Solving 2.04 + x = 2.366769951 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.04' to each side of the equation. 2.04 + -2.04 + x = 2.366769951 + -2.04 Combine like terms: 2.04 + -2.04 = 0.00 0.00 + x = 2.366769951 + -2.04 x = 2.366769951 + -2.04 Combine like terms: 2.366769951 + -2.04 = 0.326769951 x = 0.326769951 Simplifying x = 0.326769951Subproblem 2
x + 2.04 = -2.366769951 Simplifying x + 2.04 = -2.366769951 Reorder the terms: 2.04 + x = -2.366769951 Solving 2.04 + x = -2.366769951 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.04' to each side of the equation. 2.04 + -2.04 + x = -2.366769951 + -2.04 Combine like terms: 2.04 + -2.04 = 0.00 0.00 + x = -2.366769951 + -2.04 x = -2.366769951 + -2.04 Combine like terms: -2.366769951 + -2.04 = -4.406769951 x = -4.406769951 Simplifying x = -4.406769951Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.326769951, -4.406769951}
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