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Simplifying -16x2 + 17.3x + 1.5 = 10x Reorder the terms: 1.5 + 17.3x + -16x2 = 10x Solving 1.5 + 17.3x + -16x2 = 10x Solving for variable 'x'. Reorder the terms: 1.5 + 17.3x + -10x + -16x2 = 10x + -10x Combine like terms: 17.3x + -10x = 7.3x 1.5 + 7.3x + -16x2 = 10x + -10x Combine like terms: 10x + -10x = 0 1.5 + 7.3x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.09375 + -0.45625x + x2 = 0 Move the constant term to the right: Add '0.09375' to each side of the equation. -0.09375 + -0.45625x + 0.09375 + x2 = 0 + 0.09375 Reorder the terms: -0.09375 + 0.09375 + -0.45625x + x2 = 0 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + -0.45625x + x2 = 0 + 0.09375 -0.45625x + x2 = 0 + 0.09375 Combine like terms: 0 + 0.09375 = 0.09375 -0.45625x + x2 = 0.09375 The x term is -0.45625x. Take half its coefficient (-0.228125). Square it (0.05204101563) and add it to both sides. Add '0.05204101563' to each side of the equation. -0.45625x + 0.05204101563 + x2 = 0.09375 + 0.05204101563 Reorder the terms: 0.05204101563 + -0.45625x + x2 = 0.09375 + 0.05204101563 Combine like terms: 0.09375 + 0.05204101563 = 0.14579101563 0.05204101563 + -0.45625x + x2 = 0.14579101563 Factor a perfect square on the left side: (x + -0.228125)(x + -0.228125) = 0.14579101563 Calculate the square root of the right side: 0.381825897 Break this problem into two subproblems by setting (x + -0.228125) equal to 0.381825897 and -0.381825897.Subproblem 1
x + -0.228125 = 0.381825897 Simplifying x + -0.228125 = 0.381825897 Reorder the terms: -0.228125 + x = 0.381825897 Solving -0.228125 + x = 0.381825897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.228125' to each side of the equation. -0.228125 + 0.228125 + x = 0.381825897 + 0.228125 Combine like terms: -0.228125 + 0.228125 = 0.000000 0.000000 + x = 0.381825897 + 0.228125 x = 0.381825897 + 0.228125 Combine like terms: 0.381825897 + 0.228125 = 0.609950897 x = 0.609950897 Simplifying x = 0.609950897Subproblem 2
x + -0.228125 = -0.381825897 Simplifying x + -0.228125 = -0.381825897 Reorder the terms: -0.228125 + x = -0.381825897 Solving -0.228125 + x = -0.381825897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.228125' to each side of the equation. -0.228125 + 0.228125 + x = -0.381825897 + 0.228125 Combine like terms: -0.228125 + 0.228125 = 0.000000 0.000000 + x = -0.381825897 + 0.228125 x = -0.381825897 + 0.228125 Combine like terms: -0.381825897 + 0.228125 = -0.153700897 x = -0.153700897 Simplifying x = -0.153700897Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.609950897, -0.153700897}
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