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Simplifying 0 = 0.012x2 + -0.573x + -4.276 Reorder the terms: 0 = -4.276 + -0.573x + 0.012x2 Solving 0 = -4.276 + -0.573x + 0.012x2 Solving for variable 'x'. Combine like terms: 0 + 4.276 = 4.276 4.276 + 0.573x + -0.012x2 = -4.276 + -0.573x + 0.012x2 + 4.276 + 0.573x + -0.012x2 Reorder the terms: 4.276 + 0.573x + -0.012x2 = -4.276 + 4.276 + -0.573x + 0.573x + 0.012x2 + -0.012x2 Combine like terms: -4.276 + 4.276 = 0.000 4.276 + 0.573x + -0.012x2 = 0.000 + -0.573x + 0.573x + 0.012x2 + -0.012x2 4.276 + 0.573x + -0.012x2 = -0.573x + 0.573x + 0.012x2 + -0.012x2 Combine like terms: -0.573x + 0.573x = 0.000 4.276 + 0.573x + -0.012x2 = 0.000 + 0.012x2 + -0.012x2 4.276 + 0.573x + -0.012x2 = 0.012x2 + -0.012x2 Combine like terms: 0.012x2 + -0.012x2 = 0.000 4.276 + 0.573x + -0.012x2 = 0.000 Begin completing the square. Divide all terms by -0.012 the coefficient of the squared term: Divide each side by '-0.012'. -356.3333333 + -47.75x + x2 = 0 Move the constant term to the right: Add '356.3333333' to each side of the equation. -356.3333333 + -47.75x + 356.3333333 + x2 = 0 + 356.3333333 Reorder the terms: -356.3333333 + 356.3333333 + -47.75x + x2 = 0 + 356.3333333 Combine like terms: -356.3333333 + 356.3333333 = 0.0000000 0.0000000 + -47.75x + x2 = 0 + 356.3333333 -47.75x + x2 = 0 + 356.3333333 Combine like terms: 0 + 356.3333333 = 356.3333333 -47.75x + x2 = 356.3333333 The x term is -47.75x. Take half its coefficient (-23.875). Square it (570.015625) and add it to both sides. Add '570.015625' to each side of the equation. -47.75x + 570.015625 + x2 = 356.3333333 + 570.015625 Reorder the terms: 570.015625 + -47.75x + x2 = 356.3333333 + 570.015625 Combine like terms: 356.3333333 + 570.015625 = 926.3489583 570.015625 + -47.75x + x2 = 926.3489583 Factor a perfect square on the left side: (x + -23.875)(x + -23.875) = 926.3489583 Calculate the square root of the right side: 30.43598131 Break this problem into two subproblems by setting (x + -23.875) equal to 30.43598131 and -30.43598131.Subproblem 1
x + -23.875 = 30.43598131 Simplifying x + -23.875 = 30.43598131 Reorder the terms: -23.875 + x = 30.43598131 Solving -23.875 + x = 30.43598131 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23.875' to each side of the equation. -23.875 + 23.875 + x = 30.43598131 + 23.875 Combine like terms: -23.875 + 23.875 = 0.000 0.000 + x = 30.43598131 + 23.875 x = 30.43598131 + 23.875 Combine like terms: 30.43598131 + 23.875 = 54.31098131 x = 54.31098131 Simplifying x = 54.31098131Subproblem 2
x + -23.875 = -30.43598131 Simplifying x + -23.875 = -30.43598131 Reorder the terms: -23.875 + x = -30.43598131 Solving -23.875 + x = -30.43598131 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23.875' to each side of the equation. -23.875 + 23.875 + x = -30.43598131 + 23.875 Combine like terms: -23.875 + 23.875 = 0.000 0.000 + x = -30.43598131 + 23.875 x = -30.43598131 + 23.875 Combine like terms: -30.43598131 + 23.875 = -6.56098131 x = -6.56098131 Simplifying x = -6.56098131Solution
The solution to the problem is based on the solutions from the subproblems. x = {54.31098131, -6.56098131}
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