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Simplifying 2x2 + 35x = -15 Reorder the terms: 35x + 2x2 = -15 Solving 35x + 2x2 = -15 Solving for variable 'x'. Reorder the terms: 15 + 35x + 2x2 = -15 + 15 Combine like terms: -15 + 15 = 0 15 + 35x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + 17.5x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + 17.5x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + 17.5x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + 17.5x + x2 = 0 + -7.5 17.5x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 17.5x + x2 = -7.5 The x term is 17.5x. Take half its coefficient (8.75). Square it (76.5625) and add it to both sides. Add '76.5625' to each side of the equation. 17.5x + 76.5625 + x2 = -7.5 + 76.5625 Reorder the terms: 76.5625 + 17.5x + x2 = -7.5 + 76.5625 Combine like terms: -7.5 + 76.5625 = 69.0625 76.5625 + 17.5x + x2 = 69.0625 Factor a perfect square on the left side: (x + 8.75)(x + 8.75) = 69.0625 Calculate the square root of the right side: 8.310385069 Break this problem into two subproblems by setting (x + 8.75) equal to 8.310385069 and -8.310385069.Subproblem 1
x + 8.75 = 8.310385069 Simplifying x + 8.75 = 8.310385069 Reorder the terms: 8.75 + x = 8.310385069 Solving 8.75 + x = 8.310385069 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.75' to each side of the equation. 8.75 + -8.75 + x = 8.310385069 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = 8.310385069 + -8.75 x = 8.310385069 + -8.75 Combine like terms: 8.310385069 + -8.75 = -0.439614931 x = -0.439614931 Simplifying x = -0.439614931Subproblem 2
x + 8.75 = -8.310385069 Simplifying x + 8.75 = -8.310385069 Reorder the terms: 8.75 + x = -8.310385069 Solving 8.75 + x = -8.310385069 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.75' to each side of the equation. 8.75 + -8.75 + x = -8.310385069 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = -8.310385069 + -8.75 x = -8.310385069 + -8.75 Combine like terms: -8.310385069 + -8.75 = -17.060385069 x = -17.060385069 Simplifying x = -17.060385069Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.439614931, -17.060385069}
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