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Simplifying 0 = 2x2 + 13x + -35 Reorder the terms: 0 = -35 + 13x + 2x2 Solving 0 = -35 + 13x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 35 = 35 35 + -13x + -2x2 = -35 + 13x + 2x2 + 35 + -13x + -2x2 Reorder the terms: 35 + -13x + -2x2 = -35 + 35 + 13x + -13x + 2x2 + -2x2 Combine like terms: -35 + 35 = 0 35 + -13x + -2x2 = 0 + 13x + -13x + 2x2 + -2x2 35 + -13x + -2x2 = 13x + -13x + 2x2 + -2x2 Combine like terms: 13x + -13x = 0 35 + -13x + -2x2 = 0 + 2x2 + -2x2 35 + -13x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 35 + -13x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -17.5 + 6.5x + x2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + 6.5x + 17.5 + x2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + 6.5x + x2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + 6.5x + x2 = 0 + 17.5 6.5x + x2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 6.5x + x2 = 17.5 The x term is 6.5x. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5x + 10.5625 + x2 = 17.5 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = 17.5 + 10.5625 Combine like terms: 17.5 + 10.5625 = 28.0625 10.5625 + 6.5x + x2 = 28.0625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 28.0625 Calculate the square root of the right side: 5.297405025 Break this problem into two subproblems by setting (x + 3.25) equal to 5.297405025 and -5.297405025.Subproblem 1
x + 3.25 = 5.297405025 Simplifying x + 3.25 = 5.297405025 Reorder the terms: 3.25 + x = 5.297405025 Solving 3.25 + x = 5.297405025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = 5.297405025 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 5.297405025 + -3.25 x = 5.297405025 + -3.25 Combine like terms: 5.297405025 + -3.25 = 2.047405025 x = 2.047405025 Simplifying x = 2.047405025Subproblem 2
x + 3.25 = -5.297405025 Simplifying x + 3.25 = -5.297405025 Reorder the terms: 3.25 + x = -5.297405025 Solving 3.25 + x = -5.297405025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = -5.297405025 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -5.297405025 + -3.25 x = -5.297405025 + -3.25 Combine like terms: -5.297405025 + -3.25 = -8.547405025 x = -8.547405025 Simplifying x = -8.547405025Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.047405025, -8.547405025}
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