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Simplifying 5x2 + -4x + -51 = 0 Reorder the terms: -51 + -4x + 5x2 = 0 Solving -51 + -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'. -10.2 + -0.8x + x2 = 0 Move the constant term to the right: Add '10.2' to each side of the equation. -10.2 + -0.8x + 10.2 + x2 = 0 + 10.2 Reorder the terms: -10.2 + 10.2 + -0.8x + x2 = 0 + 10.2 Combine like terms: -10.2 + 10.2 = 0.0 0.0 + -0.8x + x2 = 0 + 10.2 -0.8x + x2 = 0 + 10.2 Combine like terms: 0 + 10.2 = 10.2 -0.8x + x2 = 10.2 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 = 10.2 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 10.2 + 0.16 Combine like terms: 10.2 + 0.16 = 10.36 0.16 + -0.8x + x2 = 10.36 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 10.36 Calculate the square root of the right side: 3.218695388 Break this problem into two subproblems by setting (x + -0.4) equal to 3.218695388 and -3.218695388.Subproblem 1
x + -0.4 = 3.218695388 Simplifying x + -0.4 = 3.218695388 Reorder the terms: -0.4 + x = 3.218695388 Solving -0.4 + x = 3.218695388 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 = 3.218695388 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 3.218695388 + 0.4 x = 3.218695388 + 0.4 Combine like terms: 3.218695388 + 0.4 = 3.618695388 x = 3.618695388 Simplifying x = 3.618695388Subproblem 2
x + -0.4 = -3.218695388 Simplifying x + -0.4 = -3.218695388 Reorder the terms: -0.4 + x = -3.218695388 Solving -0.4 + x = -3.218695388 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 = -3.218695388 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -3.218695388 + 0.4 x = -3.218695388 + 0.4 Combine like terms: -3.218695388 + 0.4 = -2.818695388 x = -2.818695388 Simplifying x = -2.818695388Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.618695388, -2.818695388}
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