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Simplifying 0.3125 = -16x2 + 10x Reorder the terms: 0.3125 = 10x + -16x2 Solving 0.3125 = 10x + -16x2 Solving for variable 'x'. Reorder the terms: 0.3125 + -10x + 16x2 = 10x + -10x + -16x2 + 16x2 Combine like terms: 10x + -10x = 0 0.3125 + -10x + 16x2 = 0 + -16x2 + 16x2 0.3125 + -10x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 0.3125 + -10x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.01953125 + -0.625x + x2 = 0 Move the constant term to the right: Add '-0.01953125' to each side of the equation. 0.01953125 + -0.625x + -0.01953125 + x2 = 0 + -0.01953125 Reorder the terms: 0.01953125 + -0.01953125 + -0.625x + x2 = 0 + -0.01953125 Combine like terms: 0.01953125 + -0.01953125 = 0.00000000 0.00000000 + -0.625x + x2 = 0 + -0.01953125 -0.625x + x2 = 0 + -0.01953125 Combine like terms: 0 + -0.01953125 = -0.01953125 -0.625x + x2 = -0.01953125 The x term is -0.625x. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625x + 0.09765625 + x2 = -0.01953125 + 0.09765625 Reorder the terms: 0.09765625 + -0.625x + x2 = -0.01953125 + 0.09765625 Combine like terms: -0.01953125 + 0.09765625 = 0.078125 0.09765625 + -0.625x + x2 = 0.078125 Factor a perfect square on the left side: (x + -0.3125)(x + -0.3125) = 0.078125 Calculate the square root of the right side: 0.279508497 Break this problem into two subproblems by setting (x + -0.3125) equal to 0.279508497 and -0.279508497.Subproblem 1
x + -0.3125 = 0.279508497 Simplifying x + -0.3125 = 0.279508497 Reorder the terms: -0.3125 + x = 0.279508497 Solving -0.3125 + x = 0.279508497 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = 0.279508497 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = 0.279508497 + 0.3125 x = 0.279508497 + 0.3125 Combine like terms: 0.279508497 + 0.3125 = 0.592008497 x = 0.592008497 Simplifying x = 0.592008497Subproblem 2
x + -0.3125 = -0.279508497 Simplifying x + -0.3125 = -0.279508497 Reorder the terms: -0.3125 + x = -0.279508497 Solving -0.3125 + x = -0.279508497 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = -0.279508497 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = -0.279508497 + 0.3125 x = -0.279508497 + 0.3125 Combine like terms: -0.279508497 + 0.3125 = 0.032991503 x = 0.032991503 Simplifying x = 0.032991503Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.592008497, 0.032991503}
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