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Simplifying 0.15x2 + -0.32x + -3.6 = 0 Reorder the terms: -3.6 + -0.32x + 0.15x2 = 0 Solving -3.6 + -0.32x + 0.15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.15 the coefficient of the squared term: Divide each side by '0.15'. -24 + -2.133333333x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + -2.133333333x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -2.133333333x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -2.133333333x + x2 = 0 + 24 -2.133333333x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -2.133333333x + x2 = 24 The x term is -2.133333333x. Take half its coefficient (-1.066666667). Square it (1.137777778) and add it to both sides. Add '1.137777778' to each side of the equation. -2.133333333x + 1.137777778 + x2 = 24 + 1.137777778 Reorder the terms: 1.137777778 + -2.133333333x + x2 = 24 + 1.137777778 Combine like terms: 24 + 1.137777778 = 25.137777778 1.137777778 + -2.133333333x + x2 = 25.137777778 Factor a perfect square on the left side: (x + -1.066666667)(x + -1.066666667) = 25.137777778 Calculate the square root of the right side: 5.013758847 Break this problem into two subproblems by setting (x + -1.066666667) equal to 5.013758847 and -5.013758847.Subproblem 1
x + -1.066666667 = 5.013758847 Simplifying x + -1.066666667 = 5.013758847 Reorder the terms: -1.066666667 + x = 5.013758847 Solving -1.066666667 + x = 5.013758847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.066666667' to each side of the equation. -1.066666667 + 1.066666667 + x = 5.013758847 + 1.066666667 Combine like terms: -1.066666667 + 1.066666667 = 0.000000000 0.000000000 + x = 5.013758847 + 1.066666667 x = 5.013758847 + 1.066666667 Combine like terms: 5.013758847 + 1.066666667 = 6.080425514 x = 6.080425514 Simplifying x = 6.080425514Subproblem 2
x + -1.066666667 = -5.013758847 Simplifying x + -1.066666667 = -5.013758847 Reorder the terms: -1.066666667 + x = -5.013758847 Solving -1.066666667 + x = -5.013758847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.066666667' to each side of the equation. -1.066666667 + 1.066666667 + x = -5.013758847 + 1.066666667 Combine like terms: -1.066666667 + 1.066666667 = 0.000000000 0.000000000 + x = -5.013758847 + 1.066666667 x = -5.013758847 + 1.066666667 Combine like terms: -5.013758847 + 1.066666667 = -3.94709218 x = -3.94709218 Simplifying x = -3.94709218Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.080425514, -3.94709218}
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