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Simplifying 10 = -17.92x2 + 24x + 3 Reorder the terms: 10 = 3 + 24x + -17.92x2 Solving 10 = 3 + 24x + -17.92x2 Solving for variable 'x'. Combine like terms: 10 + -3 = 7 7 + -24x + 17.92x2 = 3 + 24x + -17.92x2 + -3 + -24x + 17.92x2 Reorder the terms: 7 + -24x + 17.92x2 = 3 + -3 + 24x + -24x + -17.92x2 + 17.92x2 Combine like terms: 3 + -3 = 0 7 + -24x + 17.92x2 = 0 + 24x + -24x + -17.92x2 + 17.92x2 7 + -24x + 17.92x2 = 24x + -24x + -17.92x2 + 17.92x2 Combine like terms: 24x + -24x = 0 7 + -24x + 17.92x2 = 0 + -17.92x2 + 17.92x2 7 + -24x + 17.92x2 = -17.92x2 + 17.92x2 Combine like terms: -17.92x2 + 17.92x2 = 0.00 7 + -24x + 17.92x2 = 0.00 Begin completing the square. Divide all terms by 17.92 the coefficient of the squared term: Divide each side by '17.92'. 0.390625 + -1.339285714x + x2 = 0 Move the constant term to the right: Add '-0.390625' to each side of the equation. 0.390625 + -1.339285714x + -0.390625 + x2 = 0 + -0.390625 Reorder the terms: 0.390625 + -0.390625 + -1.339285714x + x2 = 0 + -0.390625 Combine like terms: 0.390625 + -0.390625 = 0.000000 0.000000 + -1.339285714x + x2 = 0 + -0.390625 -1.339285714x + x2 = 0 + -0.390625 Combine like terms: 0 + -0.390625 = -0.390625 -1.339285714x + x2 = -0.390625 The x term is -1.339285714x. Take half its coefficient (-0.669642857). Square it (0.4484215559) and add it to both sides. Add '0.4484215559' to each side of the equation. -1.339285714x + 0.4484215559 + x2 = -0.390625 + 0.4484215559 Reorder the terms: 0.4484215559 + -1.339285714x + x2 = -0.390625 + 0.4484215559 Combine like terms: -0.390625 + 0.4484215559 = 0.0577965559 0.4484215559 + -1.339285714x + x2 = 0.0577965559 Factor a perfect square on the left side: (x + -0.669642857)(x + -0.669642857) = 0.0577965559 Calculate the square root of the right side: 0.240409143 Break this problem into two subproblems by setting (x + -0.669642857) equal to 0.240409143 and -0.240409143.Subproblem 1
x + -0.669642857 = 0.240409143 Simplifying x + -0.669642857 = 0.240409143 Reorder the terms: -0.669642857 + x = 0.240409143 Solving -0.669642857 + x = 0.240409143 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.669642857' to each side of the equation. -0.669642857 + 0.669642857 + x = 0.240409143 + 0.669642857 Combine like terms: -0.669642857 + 0.669642857 = 0.000000000 0.000000000 + x = 0.240409143 + 0.669642857 x = 0.240409143 + 0.669642857 Combine like terms: 0.240409143 + 0.669642857 = 0.910052 x = 0.910052 Simplifying x = 0.910052Subproblem 2
x + -0.669642857 = -0.240409143 Simplifying x + -0.669642857 = -0.240409143 Reorder the terms: -0.669642857 + x = -0.240409143 Solving -0.669642857 + x = -0.240409143 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.669642857' to each side of the equation. -0.669642857 + 0.669642857 + x = -0.240409143 + 0.669642857 Combine like terms: -0.669642857 + 0.669642857 = 0.000000000 0.000000000 + x = -0.240409143 + 0.669642857 x = -0.240409143 + 0.669642857 Combine like terms: -0.240409143 + 0.669642857 = 0.429233714 x = 0.429233714 Simplifying x = 0.429233714Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.910052, 0.429233714}
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