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Simplifying 30X2 + -18X + 0.8 = 0 Reorder the terms: 0.8 + -18X + 30X2 = 0 Solving 0.8 + -18X + 30X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. 0.02666666667 + -0.6X + X2 = 0 Move the constant term to the right: Add '-0.02666666667' to each side of the equation. 0.02666666667 + -0.6X + -0.02666666667 + X2 = 0 + -0.02666666667 Reorder the terms: 0.02666666667 + -0.02666666667 + -0.6X + X2 = 0 + -0.02666666667 Combine like terms: 0.02666666667 + -0.02666666667 = 0.00000000000 0.00000000000 + -0.6X + X2 = 0 + -0.02666666667 -0.6X + X2 = 0 + -0.02666666667 Combine like terms: 0 + -0.02666666667 = -0.02666666667 -0.6X + X2 = -0.02666666667 The X term is -0.6X. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6X + 0.09 + X2 = -0.02666666667 + 0.09 Reorder the terms: 0.09 + -0.6X + X2 = -0.02666666667 + 0.09 Combine like terms: -0.02666666667 + 0.09 = 0.06333333333 0.09 + -0.6X + X2 = 0.06333333333 Factor a perfect square on the left side: (X + -0.3)(X + -0.3) = 0.06333333333 Calculate the square root of the right side: 0.251661148 Break this problem into two subproblems by setting (X + -0.3) equal to 0.251661148 and -0.251661148.Subproblem 1
X + -0.3 = 0.251661148 Simplifying X + -0.3 = 0.251661148 Reorder the terms: -0.3 + X = 0.251661148 Solving -0.3 + X = 0.251661148 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + X = 0.251661148 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + X = 0.251661148 + 0.3 X = 0.251661148 + 0.3 Combine like terms: 0.251661148 + 0.3 = 0.551661148 X = 0.551661148 Simplifying X = 0.551661148Subproblem 2
X + -0.3 = -0.251661148 Simplifying X + -0.3 = -0.251661148 Reorder the terms: -0.3 + X = -0.251661148 Solving -0.3 + X = -0.251661148 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + X = -0.251661148 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + X = -0.251661148 + 0.3 X = -0.251661148 + 0.3 Combine like terms: -0.251661148 + 0.3 = 0.048338852 X = 0.048338852 Simplifying X = 0.048338852Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.551661148, 0.048338852}
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