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Simplifying 5x2 = 51x + 54 Reorder the terms: 5x2 = 54 + 51x Solving 5x2 = 54 + 51x Solving for variable 'x'. Reorder the terms: -54 + -51x + 5x2 = 54 + 51x + -54 + -51x Reorder the terms: -54 + -51x + 5x2 = 54 + -54 + 51x + -51x Combine like terms: 54 + -54 = 0 -54 + -51x + 5x2 = 0 + 51x + -51x -54 + -51x + 5x2 = 51x + -51x Combine like terms: 51x + -51x = 0 -54 + -51x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -10.8 + -10.2x + x2 = 0 Move the constant term to the right: Add '10.8' to each side of the equation. -10.8 + -10.2x + 10.8 + x2 = 0 + 10.8 Reorder the terms: -10.8 + 10.8 + -10.2x + x2 = 0 + 10.8 Combine like terms: -10.8 + 10.8 = 0.0 0.0 + -10.2x + x2 = 0 + 10.8 -10.2x + x2 = 0 + 10.8 Combine like terms: 0 + 10.8 = 10.8 -10.2x + x2 = 10.8 The x term is -10.2x. Take half its coefficient (-5.1). Square it (26.01) and add it to both sides. Add '26.01' to each side of the equation. -10.2x + 26.01 + x2 = 10.8 + 26.01 Reorder the terms: 26.01 + -10.2x + x2 = 10.8 + 26.01 Combine like terms: 10.8 + 26.01 = 36.81 26.01 + -10.2x + x2 = 36.81 Factor a perfect square on the left side: (x + -5.1)(x + -5.1) = 36.81 Calculate the square root of the right side: 6.067124525 Break this problem into two subproblems by setting (x + -5.1) equal to 6.067124525 and -6.067124525.Subproblem 1
x + -5.1 = 6.067124525 Simplifying x + -5.1 = 6.067124525 Reorder the terms: -5.1 + x = 6.067124525 Solving -5.1 + x = 6.067124525 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.1' to each side of the equation. -5.1 + 5.1 + x = 6.067124525 + 5.1 Combine like terms: -5.1 + 5.1 = 0.0 0.0 + x = 6.067124525 + 5.1 x = 6.067124525 + 5.1 Combine like terms: 6.067124525 + 5.1 = 11.167124525 x = 11.167124525 Simplifying x = 11.167124525Subproblem 2
x + -5.1 = -6.067124525 Simplifying x + -5.1 = -6.067124525 Reorder the terms: -5.1 + x = -6.067124525 Solving -5.1 + x = -6.067124525 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.1' to each side of the equation. -5.1 + 5.1 + x = -6.067124525 + 5.1 Combine like terms: -5.1 + 5.1 = 0.0 0.0 + x = -6.067124525 + 5.1 x = -6.067124525 + 5.1 Combine like terms: -6.067124525 + 5.1 = -0.967124525 x = -0.967124525 Simplifying x = -0.967124525Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.167124525, -0.967124525}
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