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Simplifying 24x2 + -5x + -10 = 0 Reorder the terms: -10 + -5x + 24x2 = 0 Solving -10 + -5x + 24x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.4166666667 + -0.2083333333x + x2 = 0 Move the constant term to the right: Add '0.4166666667' to each side of the equation. -0.4166666667 + -0.2083333333x + 0.4166666667 + x2 = 0 + 0.4166666667 Reorder the terms: -0.4166666667 + 0.4166666667 + -0.2083333333x + x2 = 0 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + -0.2083333333x + x2 = 0 + 0.4166666667 -0.2083333333x + x2 = 0 + 0.4166666667 Combine like terms: 0 + 0.4166666667 = 0.4166666667 -0.2083333333x + x2 = 0.4166666667 The x term is -0.2083333333x. Take half its coefficient (-0.1041666667). Square it (0.01085069445) and add it to both sides. Add '0.01085069445' to each side of the equation. -0.2083333333x + 0.01085069445 + x2 = 0.4166666667 + 0.01085069445 Reorder the terms: 0.01085069445 + -0.2083333333x + x2 = 0.4166666667 + 0.01085069445 Combine like terms: 0.4166666667 + 0.01085069445 = 0.42751736115 0.01085069445 + -0.2083333333x + x2 = 0.42751736115 Factor a perfect square on the left side: (x + -0.1041666667)(x + -0.1041666667) = 0.42751736115 Calculate the square root of the right side: 0.653848118 Break this problem into two subproblems by setting (x + -0.1041666667) equal to 0.653848118 and -0.653848118.Subproblem 1
x + -0.1041666667 = 0.653848118 Simplifying x + -0.1041666667 = 0.653848118 Reorder the terms: -0.1041666667 + x = 0.653848118 Solving -0.1041666667 + x = 0.653848118 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1041666667' to each side of the equation. -0.1041666667 + 0.1041666667 + x = 0.653848118 + 0.1041666667 Combine like terms: -0.1041666667 + 0.1041666667 = 0.0000000000 0.0000000000 + x = 0.653848118 + 0.1041666667 x = 0.653848118 + 0.1041666667 Combine like terms: 0.653848118 + 0.1041666667 = 0.7580147847 x = 0.7580147847 Simplifying x = 0.7580147847Subproblem 2
x + -0.1041666667 = -0.653848118 Simplifying x + -0.1041666667 = -0.653848118 Reorder the terms: -0.1041666667 + x = -0.653848118 Solving -0.1041666667 + x = -0.653848118 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1041666667' to each side of the equation. -0.1041666667 + 0.1041666667 + x = -0.653848118 + 0.1041666667 Combine like terms: -0.1041666667 + 0.1041666667 = 0.0000000000 0.0000000000 + x = -0.653848118 + 0.1041666667 x = -0.653848118 + 0.1041666667 Combine like terms: -0.653848118 + 0.1041666667 = -0.5496814513 x = -0.5496814513 Simplifying x = -0.5496814513Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7580147847, -0.5496814513}
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