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Simplifying 2x2 + x + -53 = 0 Reorder the terms: -53 + x + 2x2 = 0 Solving -53 + x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -26.5 + 0.5x + x2 = 0 Move the constant term to the right: Add '26.5' to each side of the equation. -26.5 + 0.5x + 26.5 + x2 = 0 + 26.5 Reorder the terms: -26.5 + 26.5 + 0.5x + x2 = 0 + 26.5 Combine like terms: -26.5 + 26.5 = 0.0 0.0 + 0.5x + x2 = 0 + 26.5 0.5x + x2 = 0 + 26.5 Combine like terms: 0 + 26.5 = 26.5 0.5x + x2 = 26.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5x + 0.25 + x2 = 26.5 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 26.5 + 0.25 Combine like terms: 26.5 + 0.25 = 26.75 0.25 + 0.5x + x2 = 26.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 26.75 Calculate the square root of the right side: 5.172040216 Break this problem into two subproblems by setting (x + 0.5) equal to 5.172040216 and -5.172040216.Subproblem 1
x + 0.5 = 5.172040216 Simplifying x + 0.5 = 5.172040216 Reorder the terms: 0.5 + x = 5.172040216 Solving 0.5 + x = 5.172040216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 5.172040216 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.172040216 + -0.5 x = 5.172040216 + -0.5 Combine like terms: 5.172040216 + -0.5 = 4.672040216 x = 4.672040216 Simplifying x = 4.672040216Subproblem 2
x + 0.5 = -5.172040216 Simplifying x + 0.5 = -5.172040216 Reorder the terms: 0.5 + x = -5.172040216 Solving 0.5 + x = -5.172040216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -5.172040216 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.172040216 + -0.5 x = -5.172040216 + -0.5 Combine like terms: -5.172040216 + -0.5 = -5.672040216 x = -5.672040216 Simplifying x = -5.672040216Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.672040216, -5.672040216}
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