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Simplifying 5x2 + -12x + -54 = 0 Reorder the terms: -54 + -12x + 5x2 = 0 Solving -54 + -12x + 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 + -2.4x + x2 = 0 Move the constant term to the right: Add '10.8' to each side of the equation. -10.8 + -2.4x + 10.8 + x2 = 0 + 10.8 Reorder the terms: -10.8 + 10.8 + -2.4x + x2 = 0 + 10.8 Combine like terms: -10.8 + 10.8 = 0.0 0.0 + -2.4x + x2 = 0 + 10.8 -2.4x + x2 = 0 + 10.8 Combine like terms: 0 + 10.8 = 10.8 -2.4x + x2 = 10.8 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = 10.8 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = 10.8 + 1.44 Combine like terms: 10.8 + 1.44 = 12.24 1.44 + -2.4x + x2 = 12.24 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 12.24 Calculate the square root of the right side: 3.498571137 Break this problem into two subproblems by setting (x + -1.2) equal to 3.498571137 and -3.498571137.Subproblem 1
x + -1.2 = 3.498571137 Simplifying x + -1.2 = 3.498571137 Reorder the terms: -1.2 + x = 3.498571137 Solving -1.2 + x = 3.498571137 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 3.498571137 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 3.498571137 + 1.2 x = 3.498571137 + 1.2 Combine like terms: 3.498571137 + 1.2 = 4.698571137 x = 4.698571137 Simplifying x = 4.698571137Subproblem 2
x + -1.2 = -3.498571137 Simplifying x + -1.2 = -3.498571137 Reorder the terms: -1.2 + x = -3.498571137 Solving -1.2 + x = -3.498571137 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -3.498571137 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -3.498571137 + 1.2 x = -3.498571137 + 1.2 Combine like terms: -3.498571137 + 1.2 = -2.298571137 x = -2.298571137 Simplifying x = -2.298571137Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.698571137, -2.298571137}
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