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Simplifying 5x2 + -71x + -282 = 0 Reorder the terms: -282 + -71x + 5x2 = 0 Solving -282 + -71x + 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'. -56.4 + -14.2x + x2 = 0 Move the constant term to the right: Add '56.4' to each side of the equation. -56.4 + -14.2x + 56.4 + x2 = 0 + 56.4 Reorder the terms: -56.4 + 56.4 + -14.2x + x2 = 0 + 56.4 Combine like terms: -56.4 + 56.4 = 0.0 0.0 + -14.2x + x2 = 0 + 56.4 -14.2x + x2 = 0 + 56.4 Combine like terms: 0 + 56.4 = 56.4 -14.2x + x2 = 56.4 The x term is -14.2x. Take half its coefficient (-7.1). Square it (50.41) and add it to both sides. Add '50.41' to each side of the equation. -14.2x + 50.41 + x2 = 56.4 + 50.41 Reorder the terms: 50.41 + -14.2x + x2 = 56.4 + 50.41 Combine like terms: 56.4 + 50.41 = 106.81 50.41 + -14.2x + x2 = 106.81 Factor a perfect square on the left side: (x + -7.1)(x + -7.1) = 106.81 Calculate the square root of the right side: 10.334892356 Break this problem into two subproblems by setting (x + -7.1) equal to 10.334892356 and -10.334892356.Subproblem 1
x + -7.1 = 10.334892356 Simplifying x + -7.1 = 10.334892356 Reorder the terms: -7.1 + x = 10.334892356 Solving -7.1 + x = 10.334892356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.1' to each side of the equation. -7.1 + 7.1 + x = 10.334892356 + 7.1 Combine like terms: -7.1 + 7.1 = 0.0 0.0 + x = 10.334892356 + 7.1 x = 10.334892356 + 7.1 Combine like terms: 10.334892356 + 7.1 = 17.434892356 x = 17.434892356 Simplifying x = 17.434892356Subproblem 2
x + -7.1 = -10.334892356 Simplifying x + -7.1 = -10.334892356 Reorder the terms: -7.1 + x = -10.334892356 Solving -7.1 + x = -10.334892356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.1' to each side of the equation. -7.1 + 7.1 + x = -10.334892356 + 7.1 Combine like terms: -7.1 + 7.1 = 0.0 0.0 + x = -10.334892356 + 7.1 x = -10.334892356 + 7.1 Combine like terms: -10.334892356 + 7.1 = -3.234892356 x = -3.234892356 Simplifying x = -3.234892356Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.434892356, -3.234892356}
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