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Simplifying 5x2 = 3x + 64 Reorder the terms: 5x2 = 64 + 3x Solving 5x2 = 64 + 3x Solving for variable 'x'. Reorder the terms: -64 + -3x + 5x2 = 64 + 3x + -64 + -3x Reorder the terms: -64 + -3x + 5x2 = 64 + -64 + 3x + -3x Combine like terms: 64 + -64 = 0 -64 + -3x + 5x2 = 0 + 3x + -3x -64 + -3x + 5x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -64 + -3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -12.8 + -0.6x + x2 = 0 Move the constant term to the right: Add '12.8' to each side of the equation. -12.8 + -0.6x + 12.8 + x2 = 0 + 12.8 Reorder the terms: -12.8 + 12.8 + -0.6x + x2 = 0 + 12.8 Combine like terms: -12.8 + 12.8 = 0.0 0.0 + -0.6x + x2 = 0 + 12.8 -0.6x + x2 = 0 + 12.8 Combine like terms: 0 + 12.8 = 12.8 -0.6x + x2 = 12.8 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 12.8 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 12.8 + 0.09 Combine like terms: 12.8 + 0.09 = 12.89 0.09 + -0.6x + x2 = 12.89 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 12.89 Calculate the square root of the right side: 3.590264614 Break this problem into two subproblems by setting (x + -0.3) equal to 3.590264614 and -3.590264614.Subproblem 1
x + -0.3 = 3.590264614 Simplifying x + -0.3 = 3.590264614 Reorder the terms: -0.3 + x = 3.590264614 Solving -0.3 + x = 3.590264614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 3.590264614 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 3.590264614 + 0.3 x = 3.590264614 + 0.3 Combine like terms: 3.590264614 + 0.3 = 3.890264614 x = 3.890264614 Simplifying x = 3.890264614Subproblem 2
x + -0.3 = -3.590264614 Simplifying x + -0.3 = -3.590264614 Reorder the terms: -0.3 + x = -3.590264614 Solving -0.3 + x = -3.590264614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -3.590264614 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -3.590264614 + 0.3 x = -3.590264614 + 0.3 Combine like terms: -3.590264614 + 0.3 = -3.290264614 x = -3.290264614 Simplifying x = -3.290264614Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.890264614, -3.290264614}
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