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Simplifying 5x2 + -4x + -64.01 = 0 Reorder the terms: -64.01 + -4x + 5x2 = 0 Solving -64.01 + -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'. -12.802 + -0.8x + x2 = 0 Move the constant term to the right: Add '12.802' to each side of the equation. -12.802 + -0.8x + 12.802 + x2 = 0 + 12.802 Reorder the terms: -12.802 + 12.802 + -0.8x + x2 = 0 + 12.802 Combine like terms: -12.802 + 12.802 = 0.000 0.000 + -0.8x + x2 = 0 + 12.802 -0.8x + x2 = 0 + 12.802 Combine like terms: 0 + 12.802 = 12.802 -0.8x + x2 = 12.802 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 = 12.802 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 12.802 + 0.16 Combine like terms: 12.802 + 0.16 = 12.962 0.16 + -0.8x + x2 = 12.962 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 12.962 Calculate the square root of the right side: 3.600277767 Break this problem into two subproblems by setting (x + -0.4) equal to 3.600277767 and -3.600277767.Subproblem 1
x + -0.4 = 3.600277767 Simplifying x + -0.4 = 3.600277767 Reorder the terms: -0.4 + x = 3.600277767 Solving -0.4 + x = 3.600277767 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 = 3.600277767 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 3.600277767 + 0.4 x = 3.600277767 + 0.4 Combine like terms: 3.600277767 + 0.4 = 4.000277767 x = 4.000277767 Simplifying x = 4.000277767Subproblem 2
x + -0.4 = -3.600277767 Simplifying x + -0.4 = -3.600277767 Reorder the terms: -0.4 + x = -3.600277767 Solving -0.4 + x = -3.600277767 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 = -3.600277767 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -3.600277767 + 0.4 x = -3.600277767 + 0.4 Combine like terms: -3.600277767 + 0.4 = -3.200277767 x = -3.200277767 Simplifying x = -3.200277767Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.000277767, -3.200277767}
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