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Simplifying -0.9x2 + 5.4x + 5.7 = 0 Reorder the terms: 5.7 + 5.4x + -0.9x2 = 0 Solving 5.7 + 5.4x + -0.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.9 the coefficient of the squared term: Divide each side by '-0.9'. -6.333333333 + -6x + x2 = 0 Move the constant term to the right: Add '6.333333333' to each side of the equation. -6.333333333 + -6x + 6.333333333 + x2 = 0 + 6.333333333 Reorder the terms: -6.333333333 + 6.333333333 + -6x + x2 = 0 + 6.333333333 Combine like terms: -6.333333333 + 6.333333333 = 0.000000000 0.000000000 + -6x + x2 = 0 + 6.333333333 -6x + x2 = 0 + 6.333333333 Combine like terms: 0 + 6.333333333 = 6.333333333 -6x + x2 = 6.333333333 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 6.333333333 + 9 Reorder the terms: 9 + -6x + x2 = 6.333333333 + 9 Combine like terms: 6.333333333 + 9 = 15.333333333 9 + -6x + x2 = 15.333333333 Factor a perfect square on the left side: (x + -3)(x + -3) = 15.333333333 Calculate the square root of the right side: 3.915780041 Break this problem into two subproblems by setting (x + -3) equal to 3.915780041 and -3.915780041.Subproblem 1
x + -3 = 3.915780041 Simplifying x + -3 = 3.915780041 Reorder the terms: -3 + x = 3.915780041 Solving -3 + x = 3.915780041 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.915780041 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.915780041 + 3 x = 3.915780041 + 3 Combine like terms: 3.915780041 + 3 = 6.915780041 x = 6.915780041 Simplifying x = 6.915780041Subproblem 2
x + -3 = -3.915780041 Simplifying x + -3 = -3.915780041 Reorder the terms: -3 + x = -3.915780041 Solving -3 + x = -3.915780041 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.915780041 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.915780041 + 3 x = -3.915780041 + 3 Combine like terms: -3.915780041 + 3 = -0.915780041 x = -0.915780041 Simplifying x = -0.915780041Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.915780041, -0.915780041}
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