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Simplifying 5X2 + 30X = 12 Reorder the terms: 30X + 5X2 = 12 Solving 30X + 5X2 = 12 Solving for variable 'X'. Reorder the terms: -12 + 30X + 5X2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 30X + 5X2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.4 + 6X + X2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + 6X + 2.4 + X2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + 6X + X2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + 6X + X2 = 0 + 2.4 6X + X2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 6X + X2 = 2.4 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 = 2.4 + 9 Reorder the terms: 9 + 6X + X2 = 2.4 + 9 Combine like terms: 2.4 + 9 = 11.4 9 + 6X + X2 = 11.4 Factor a perfect square on the left side: (X + 3)(X + 3) = 11.4 Calculate the square root of the right side: 3.376388603 Break this problem into two subproblems by setting (X + 3) equal to 3.376388603 and -3.376388603.Subproblem 1
X + 3 = 3.376388603 Simplifying X + 3 = 3.376388603 Reorder the terms: 3 + X = 3.376388603 Solving 3 + X = 3.376388603 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 = 3.376388603 + -3 Combine like terms: 3 + -3 = 0 0 + X = 3.376388603 + -3 X = 3.376388603 + -3 Combine like terms: 3.376388603 + -3 = 0.376388603 X = 0.376388603 Simplifying X = 0.376388603Subproblem 2
X + 3 = -3.376388603 Simplifying X + 3 = -3.376388603 Reorder the terms: 3 + X = -3.376388603 Solving 3 + X = -3.376388603 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 = -3.376388603 + -3 Combine like terms: 3 + -3 = 0 0 + X = -3.376388603 + -3 X = -3.376388603 + -3 Combine like terms: -3.376388603 + -3 = -6.376388603 X = -6.376388603 Simplifying X = -6.376388603Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.376388603, -6.376388603}
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