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Simplifying -0.0625x2 + 2x + 10 = 0 Reorder the terms: 10 + 2x + -0.0625x2 = 0 Solving 10 + 2x + -0.0625x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.0625 the coefficient of the squared term: Divide each side by '-0.0625'. -160 + -32x + x2 = 0 Move the constant term to the right: Add '160' to each side of the equation. -160 + -32x + 160 + x2 = 0 + 160 Reorder the terms: -160 + 160 + -32x + x2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + -32x + x2 = 0 + 160 -32x + x2 = 0 + 160 Combine like terms: 0 + 160 = 160 -32x + x2 = 160 The x term is -32x. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x + 256 + x2 = 160 + 256 Reorder the terms: 256 + -32x + x2 = 160 + 256 Combine like terms: 160 + 256 = 416 256 + -32x + x2 = 416 Factor a perfect square on the left side: (x + -16)(x + -16) = 416 Calculate the square root of the right side: 20.396078054 Break this problem into two subproblems by setting (x + -16) equal to 20.396078054 and -20.396078054.Subproblem 1
x + -16 = 20.396078054 Simplifying x + -16 = 20.396078054 Reorder the terms: -16 + x = 20.396078054 Solving -16 + x = 20.396078054 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 20.396078054 + 16 Combine like terms: -16 + 16 = 0 0 + x = 20.396078054 + 16 x = 20.396078054 + 16 Combine like terms: 20.396078054 + 16 = 36.396078054 x = 36.396078054 Simplifying x = 36.396078054Subproblem 2
x + -16 = -20.396078054 Simplifying x + -16 = -20.396078054 Reorder the terms: -16 + x = -20.396078054 Solving -16 + x = -20.396078054 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -20.396078054 + 16 Combine like terms: -16 + 16 = 0 0 + x = -20.396078054 + 16 x = -20.396078054 + 16 Combine like terms: -20.396078054 + 16 = -4.396078054 x = -4.396078054 Simplifying x = -4.396078054Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.396078054, -4.396078054}
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