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Simplifying 64x + -0.42x2 = 390 + 24x Solving 64x + -0.42x2 = 390 + 24x Solving for variable 'x'. Reorder the terms: -390 + 64x + -24x + -0.42x2 = 390 + 24x + -390 + -24x Combine like terms: 64x + -24x = 40x -390 + 40x + -0.42x2 = 390 + 24x + -390 + -24x Reorder the terms: -390 + 40x + -0.42x2 = 390 + -390 + 24x + -24x Combine like terms: 390 + -390 = 0 -390 + 40x + -0.42x2 = 0 + 24x + -24x -390 + 40x + -0.42x2 = 24x + -24x Combine like terms: 24x + -24x = 0 -390 + 40x + -0.42x2 = 0 Begin completing the square. Divide all terms by -0.42 the coefficient of the squared term: Divide each side by '-0.42'. 928.5714286 + -95.23809524x + x2 = 0 Move the constant term to the right: Add '-928.5714286' to each side of the equation. 928.5714286 + -95.23809524x + -928.5714286 + x2 = 0 + -928.5714286 Reorder the terms: 928.5714286 + -928.5714286 + -95.23809524x + x2 = 0 + -928.5714286 Combine like terms: 928.5714286 + -928.5714286 = 0.0000000 0.0000000 + -95.23809524x + x2 = 0 + -928.5714286 -95.23809524x + x2 = 0 + -928.5714286 Combine like terms: 0 + -928.5714286 = -928.5714286 -95.23809524x + x2 = -928.5714286 The x term is -95.23809524x. Take half its coefficient (-47.61904762). Square it (2267.573696) and add it to both sides. Add '2267.573696' to each side of the equation. -95.23809524x + 2267.573696 + x2 = -928.5714286 + 2267.573696 Reorder the terms: 2267.573696 + -95.23809524x + x2 = -928.5714286 + 2267.573696 Combine like terms: -928.5714286 + 2267.573696 = 1339.0022674 2267.573696 + -95.23809524x + x2 = 1339.0022674 Factor a perfect square on the left side: (x + -47.61904762)(x + -47.61904762) = 1339.0022674 Calculate the square root of the right side: 36.592379909 Break this problem into two subproblems by setting (x + -47.61904762) equal to 36.592379909 and -36.592379909.Subproblem 1
x + -47.61904762 = 36.592379909 Simplifying x + -47.61904762 = 36.592379909 Reorder the terms: -47.61904762 + x = 36.592379909 Solving -47.61904762 + x = 36.592379909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '47.61904762' to each side of the equation. -47.61904762 + 47.61904762 + x = 36.592379909 + 47.61904762 Combine like terms: -47.61904762 + 47.61904762 = 0.00000000 0.00000000 + x = 36.592379909 + 47.61904762 x = 36.592379909 + 47.61904762 Combine like terms: 36.592379909 + 47.61904762 = 84.211427529 x = 84.211427529 Simplifying x = 84.211427529Subproblem 2
x + -47.61904762 = -36.592379909 Simplifying x + -47.61904762 = -36.592379909 Reorder the terms: -47.61904762 + x = -36.592379909 Solving -47.61904762 + x = -36.592379909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '47.61904762' to each side of the equation. -47.61904762 + 47.61904762 + x = -36.592379909 + 47.61904762 Combine like terms: -47.61904762 + 47.61904762 = 0.00000000 0.00000000 + x = -36.592379909 + 47.61904762 x = -36.592379909 + 47.61904762 Combine like terms: -36.592379909 + 47.61904762 = 11.026667711 x = 11.026667711 Simplifying x = 11.026667711Solution
The solution to the problem is based on the solutions from the subproblems. x = {84.211427529, 11.026667711}
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