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Simplifying 0 = -0.08x2 + 1.4x + 35 Reorder the terms: 0 = 35 + 1.4x + -0.08x2 Solving 0 = 35 + 1.4x + -0.08x2 Solving for variable 'x'. Combine like terms: 0 + -35 = -35 -35 + -1.4x + 0.08x2 = 35 + 1.4x + -0.08x2 + -35 + -1.4x + 0.08x2 Reorder the terms: -35 + -1.4x + 0.08x2 = 35 + -35 + 1.4x + -1.4x + -0.08x2 + 0.08x2 Combine like terms: 35 + -35 = 0 -35 + -1.4x + 0.08x2 = 0 + 1.4x + -1.4x + -0.08x2 + 0.08x2 -35 + -1.4x + 0.08x2 = 1.4x + -1.4x + -0.08x2 + 0.08x2 Combine like terms: 1.4x + -1.4x = 0.0 -35 + -1.4x + 0.08x2 = 0.0 + -0.08x2 + 0.08x2 -35 + -1.4x + 0.08x2 = -0.08x2 + 0.08x2 Combine like terms: -0.08x2 + 0.08x2 = 0.00 -35 + -1.4x + 0.08x2 = 0.00 Begin completing the square. Divide all terms by 0.08 the coefficient of the squared term: Divide each side by '0.08'. -437.5 + -17.5x + x2 = 0 Move the constant term to the right: Add '437.5' to each side of the equation. -437.5 + -17.5x + 437.5 + x2 = 0 + 437.5 Reorder the terms: -437.5 + 437.5 + -17.5x + x2 = 0 + 437.5 Combine like terms: -437.5 + 437.5 = 0.0 0.0 + -17.5x + x2 = 0 + 437.5 -17.5x + x2 = 0 + 437.5 Combine like terms: 0 + 437.5 = 437.5 -17.5x + x2 = 437.5 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 = 437.5 + 76.5625 Reorder the terms: 76.5625 + -17.5x + x2 = 437.5 + 76.5625 Combine like terms: 437.5 + 76.5625 = 514.0625 76.5625 + -17.5x + x2 = 514.0625 Factor a perfect square on the left side: (x + -8.75)(x + -8.75) = 514.0625 Calculate the square root of the right side: 22.672946434 Break this problem into two subproblems by setting (x + -8.75) equal to 22.672946434 and -22.672946434.Subproblem 1
x + -8.75 = 22.672946434 Simplifying x + -8.75 = 22.672946434 Reorder the terms: -8.75 + x = 22.672946434 Solving -8.75 + x = 22.672946434 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 = 22.672946434 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + x = 22.672946434 + 8.75 x = 22.672946434 + 8.75 Combine like terms: 22.672946434 + 8.75 = 31.422946434 x = 31.422946434 Simplifying x = 31.422946434Subproblem 2
x + -8.75 = -22.672946434 Simplifying x + -8.75 = -22.672946434 Reorder the terms: -8.75 + x = -22.672946434 Solving -8.75 + x = -22.672946434 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 = -22.672946434 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + x = -22.672946434 + 8.75 x = -22.672946434 + 8.75 Combine like terms: -22.672946434 + 8.75 = -13.922946434 x = -13.922946434 Simplifying x = -13.922946434Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.422946434, -13.922946434}
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