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Simplifying 4x2 + 24x + -115 = 0 Reorder the terms: -115 + 24x + 4x2 = 0 Solving -115 + 24x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -28.75 + 6x + x2 = 0 Move the constant term to the right: Add '28.75' to each side of the equation. -28.75 + 6x + 28.75 + x2 = 0 + 28.75 Reorder the terms: -28.75 + 28.75 + 6x + x2 = 0 + 28.75 Combine like terms: -28.75 + 28.75 = 0.00 0.00 + 6x + x2 = 0 + 28.75 6x + x2 = 0 + 28.75 Combine like terms: 0 + 28.75 = 28.75 6x + x2 = 28.75 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 = 28.75 + 9 Reorder the terms: 9 + 6x + x2 = 28.75 + 9 Combine like terms: 28.75 + 9 = 37.75 9 + 6x + x2 = 37.75 Factor a perfect square on the left side: (x + 3)(x + 3) = 37.75 Calculate the square root of the right side: 6.144102864 Break this problem into two subproblems by setting (x + 3) equal to 6.144102864 and -6.144102864.Subproblem 1
x + 3 = 6.144102864 Simplifying x + 3 = 6.144102864 Reorder the terms: 3 + x = 6.144102864 Solving 3 + x = 6.144102864 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 = 6.144102864 + -3 Combine like terms: 3 + -3 = 0 0 + x = 6.144102864 + -3 x = 6.144102864 + -3 Combine like terms: 6.144102864 + -3 = 3.144102864 x = 3.144102864 Simplifying x = 3.144102864Subproblem 2
x + 3 = -6.144102864 Simplifying x + 3 = -6.144102864 Reorder the terms: 3 + x = -6.144102864 Solving 3 + x = -6.144102864 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 = -6.144102864 + -3 Combine like terms: 3 + -3 = 0 0 + x = -6.144102864 + -3 x = -6.144102864 + -3 Combine like terms: -6.144102864 + -3 = -9.144102864 x = -9.144102864 Simplifying x = -9.144102864Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.144102864, -9.144102864}
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