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Simplifying 5x2 + -36x + -16 = 0 Reorder the terms: -16 + -36x + 5x2 = 0 Solving -16 + -36x + 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'. -3.2 + -7.2x + x2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + -7.2x + 3.2 + x2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + -7.2x + x2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + -7.2x + x2 = 0 + 3.2 -7.2x + x2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 -7.2x + x2 = 3.2 The x term is -7.2x. Take half its coefficient (-3.6). Square it (12.96) and add it to both sides. Add '12.96' to each side of the equation. -7.2x + 12.96 + x2 = 3.2 + 12.96 Reorder the terms: 12.96 + -7.2x + x2 = 3.2 + 12.96 Combine like terms: 3.2 + 12.96 = 16.16 12.96 + -7.2x + x2 = 16.16 Factor a perfect square on the left side: (x + -3.6)(x + -3.6) = 16.16 Calculate the square root of the right side: 4.019950248 Break this problem into two subproblems by setting (x + -3.6) equal to 4.019950248 and -4.019950248.Subproblem 1
x + -3.6 = 4.019950248 Simplifying x + -3.6 = 4.019950248 Reorder the terms: -3.6 + x = 4.019950248 Solving -3.6 + x = 4.019950248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + x = 4.019950248 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x = 4.019950248 + 3.6 x = 4.019950248 + 3.6 Combine like terms: 4.019950248 + 3.6 = 7.619950248 x = 7.619950248 Simplifying x = 7.619950248Subproblem 2
x + -3.6 = -4.019950248 Simplifying x + -3.6 = -4.019950248 Reorder the terms: -3.6 + x = -4.019950248 Solving -3.6 + x = -4.019950248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + x = -4.019950248 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x = -4.019950248 + 3.6 x = -4.019950248 + 3.6 Combine like terms: -4.019950248 + 3.6 = -0.419950248 x = -0.419950248 Simplifying x = -0.419950248Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.619950248, -0.419950248}
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