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Simplifying 2x2 + 35x + -5.3 = 0 Reorder the terms: -5.3 + 35x + 2x2 = 0 Solving -5.3 + 35x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.65 + 17.5x + x2 = 0 Move the constant term to the right: Add '2.65' to each side of the equation. -2.65 + 17.5x + 2.65 + x2 = 0 + 2.65 Reorder the terms: -2.65 + 2.65 + 17.5x + x2 = 0 + 2.65 Combine like terms: -2.65 + 2.65 = 0.00 0.00 + 17.5x + x2 = 0 + 2.65 17.5x + x2 = 0 + 2.65 Combine like terms: 0 + 2.65 = 2.65 17.5x + x2 = 2.65 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 = 2.65 + 76.5625 Reorder the terms: 76.5625 + 17.5x + x2 = 2.65 + 76.5625 Combine like terms: 2.65 + 76.5625 = 79.2125 76.5625 + 17.5x + x2 = 79.2125 Factor a perfect square on the left side: (x + 8.75)(x + 8.75) = 79.2125 Calculate the square root of the right side: 8.900140448 Break this problem into two subproblems by setting (x + 8.75) equal to 8.900140448 and -8.900140448.Subproblem 1
x + 8.75 = 8.900140448 Simplifying x + 8.75 = 8.900140448 Reorder the terms: 8.75 + x = 8.900140448 Solving 8.75 + x = 8.900140448 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 = 8.900140448 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = 8.900140448 + -8.75 x = 8.900140448 + -8.75 Combine like terms: 8.900140448 + -8.75 = 0.150140448 x = 0.150140448 Simplifying x = 0.150140448Subproblem 2
x + 8.75 = -8.900140448 Simplifying x + 8.75 = -8.900140448 Reorder the terms: 8.75 + x = -8.900140448 Solving 8.75 + x = -8.900140448 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 = -8.900140448 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = -8.900140448 + -8.75 x = -8.900140448 + -8.75 Combine like terms: -8.900140448 + -8.75 = -17.650140448 x = -17.650140448 Simplifying x = -17.650140448Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.150140448, -17.650140448}
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