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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 = 2.666666667 9 + -6x + x2 = 2.666666667 Factor a perfect square on the left side: (x + -3)(x + -3) = 2.666666667 Calculate the square root of the right side: 1.632993162 Break this problem into two subproblems by setting (x + -3) equal to 1.632993162 and -1.632993162.Subproblem 1
x + -3 = 1.632993162 Simplifying x + -3 = 1.632993162 Reorder the terms: -3 + x = 1.632993162 Solving -3 + x = 1.632993162 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 = 1.632993162 + 3 Combine like terms: -3 + 3 = 0 0 + x = 1.632993162 + 3 x = 1.632993162 + 3 Combine like terms: 1.632993162 + 3 = 4.632993162 x = 4.632993162 Simplifying x = 4.632993162Subproblem 2
x + -3 = -1.632993162 Simplifying x + -3 = -1.632993162 Reorder the terms: -3 + x = -1.632993162 Solving -3 + x = -1.632993162 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 = -1.632993162 + 3 Combine like terms: -3 + 3 = 0 0 + x = -1.632993162 + 3 x = -1.632993162 + 3 Combine like terms: -1.632993162 + 3 = 1.367006838 x = 1.367006838 Simplifying x = 1.367006838Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.632993162, 1.367006838}
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