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Simplifying 5x2 + -4x + -74 = 0 Reorder the terms: -74 + -4x + 5x2 = 0 Solving -74 + -4x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -14.8 + -0.8x + x2 = 0 Move the constant term to the right: Add '14.8' to each side of the equation. -14.8 + -0.8x + 14.8 + x2 = 0 + 14.8 Reorder the terms: -14.8 + 14.8 + -0.8x + x2 = 0 + 14.8 Combine like terms: -14.8 + 14.8 = 0.0 0.0 + -0.8x + x2 = 0 + 14.8 -0.8x + x2 = 0 + 14.8 Combine like terms: 0 + 14.8 = 14.8 -0.8x + x2 = 14.8 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 14.8 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 14.8 + 0.16 Combine like terms: 14.8 + 0.16 = 14.96 0.16 + -0.8x + x2 = 14.96 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 14.96 Calculate the square root of the right side: 3.867815921 Break this problem into two subproblems by setting (x + -0.4) equal to 3.867815921 and -3.867815921.Subproblem 1
x + -0.4 = 3.867815921 Simplifying x + -0.4 = 3.867815921 Reorder the terms: -0.4 + x = 3.867815921 Solving -0.4 + x = 3.867815921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 3.867815921 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 3.867815921 + 0.4 x = 3.867815921 + 0.4 Combine like terms: 3.867815921 + 0.4 = 4.267815921 x = 4.267815921 Simplifying x = 4.267815921Subproblem 2
x + -0.4 = -3.867815921 Simplifying x + -0.4 = -3.867815921 Reorder the terms: -0.4 + x = -3.867815921 Solving -0.4 + x = -3.867815921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -3.867815921 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -3.867815921 + 0.4 x = -3.867815921 + 0.4 Combine like terms: -3.867815921 + 0.4 = -3.467815921 x = -3.467815921 Simplifying x = -3.467815921Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.267815921, -3.467815921}
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