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Simplifying 5x2 + 51x + -54 = 0 Reorder the terms: -54 + 51x + 5x2 = 0 Solving -54 + 51x + 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'. -10.8 + 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 = 0.967124525 x = 0.967124525 Simplifying x = 0.967124525Subproblem 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 = -11.167124525 x = -11.167124525 Simplifying x = -11.167124525Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.967124525, -11.167124525}
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