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Simplifying 5x2 + -54x + -63 = 0 Reorder the terms: -63 + -54x + 5x2 = 0 Solving -63 + -54x + 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'. -12.6 + -10.8x + x2 = 0 Move the constant term to the right: Add '12.6' to each side of the equation. -12.6 + -10.8x + 12.6 + x2 = 0 + 12.6 Reorder the terms: -12.6 + 12.6 + -10.8x + x2 = 0 + 12.6 Combine like terms: -12.6 + 12.6 = 0.0 0.0 + -10.8x + x2 = 0 + 12.6 -10.8x + x2 = 0 + 12.6 Combine like terms: 0 + 12.6 = 12.6 -10.8x + x2 = 12.6 The x term is -10.8x. Take half its coefficient (-5.4). Square it (29.16) and add it to both sides. Add '29.16' to each side of the equation. -10.8x + 29.16 + x2 = 12.6 + 29.16 Reorder the terms: 29.16 + -10.8x + x2 = 12.6 + 29.16 Combine like terms: 12.6 + 29.16 = 41.76 29.16 + -10.8x + x2 = 41.76 Factor a perfect square on the left side: (x + -5.4)(x + -5.4) = 41.76 Calculate the square root of the right side: 6.462197769 Break this problem into two subproblems by setting (x + -5.4) equal to 6.462197769 and -6.462197769.Subproblem 1
x + -5.4 = 6.462197769 Simplifying x + -5.4 = 6.462197769 Reorder the terms: -5.4 + x = 6.462197769 Solving -5.4 + x = 6.462197769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.4' to each side of the equation. -5.4 + 5.4 + x = 6.462197769 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + x = 6.462197769 + 5.4 x = 6.462197769 + 5.4 Combine like terms: 6.462197769 + 5.4 = 11.862197769 x = 11.862197769 Simplifying x = 11.862197769Subproblem 2
x + -5.4 = -6.462197769 Simplifying x + -5.4 = -6.462197769 Reorder the terms: -5.4 + x = -6.462197769 Solving -5.4 + x = -6.462197769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.4' to each side of the equation. -5.4 + 5.4 + x = -6.462197769 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + x = -6.462197769 + 5.4 x = -6.462197769 + 5.4 Combine like terms: -6.462197769 + 5.4 = -1.062197769 x = -1.062197769 Simplifying x = -1.062197769Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.862197769, -1.062197769}
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