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Simplifying 5x2 + 24 = 30x Reorder the terms: 24 + 5x2 = 30x Solving 24 + 5x2 = 30x Solving for variable 'x'. Reorder the terms: 24 + -30x + 5x2 = 30x + -30x Combine like terms: 30x + -30x = 0 24 + -30x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 4.8 + -6x + x2 = 0 Move the constant term to the right: Add '-4.8' to each side of the equation. 4.8 + -6x + -4.8 + x2 = 0 + -4.8 Reorder the terms: 4.8 + -4.8 + -6x + x2 = 0 + -4.8 Combine like terms: 4.8 + -4.8 = 0.0 0.0 + -6x + x2 = 0 + -4.8 -6x + x2 = 0 + -4.8 Combine like terms: 0 + -4.8 = -4.8 -6x + x2 = -4.8 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 = -4.8 + 9 Reorder the terms: 9 + -6x + x2 = -4.8 + 9 Combine like terms: -4.8 + 9 = 4.2 9 + -6x + x2 = 4.2 Factor a perfect square on the left side: (x + -3)(x + -3) = 4.2 Calculate the square root of the right side: 2.049390153 Break this problem into two subproblems by setting (x + -3) equal to 2.049390153 and -2.049390153.Subproblem 1
x + -3 = 2.049390153 Simplifying x + -3 = 2.049390153 Reorder the terms: -3 + x = 2.049390153 Solving -3 + x = 2.049390153 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 = 2.049390153 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.049390153 + 3 x = 2.049390153 + 3 Combine like terms: 2.049390153 + 3 = 5.049390153 x = 5.049390153 Simplifying x = 5.049390153Subproblem 2
x + -3 = -2.049390153 Simplifying x + -3 = -2.049390153 Reorder the terms: -3 + x = -2.049390153 Solving -3 + x = -2.049390153 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 = -2.049390153 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.049390153 + 3 x = -2.049390153 + 3 Combine like terms: -2.049390153 + 3 = 0.950609847 x = 0.950609847 Simplifying x = 0.950609847Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.049390153, 0.950609847}
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