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Simplifying -4x2 + -24x + 5 = 0 Reorder the terms: 5 + -24x + -4x2 = 0 Solving 5 + -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'. -1.25 + 6x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 6x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 6x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 6x + x2 = 0 + 1.25 6x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 6x + x2 = 1.25 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 = 1.25 + 9 Reorder the terms: 9 + 6x + x2 = 1.25 + 9 Combine like terms: 1.25 + 9 = 10.25 9 + 6x + x2 = 10.25 Factor a perfect square on the left side: (x + 3)(x + 3) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (x + 3) equal to 3.201562119 and -3.201562119.Subproblem 1
x + 3 = 3.201562119 Simplifying x + 3 = 3.201562119 Reorder the terms: 3 + x = 3.201562119 Solving 3 + x = 3.201562119 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 = 3.201562119 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.201562119 + -3 x = 3.201562119 + -3 Combine like terms: 3.201562119 + -3 = 0.201562119 x = 0.201562119 Simplifying x = 0.201562119Subproblem 2
x + 3 = -3.201562119 Simplifying x + 3 = -3.201562119 Reorder the terms: 3 + x = -3.201562119 Solving 3 + x = -3.201562119 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 = -3.201562119 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.201562119 + -3 x = -3.201562119 + -3 Combine like terms: -3.201562119 + -3 = -6.201562119 x = -6.201562119 Simplifying x = -6.201562119Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.201562119, -6.201562119}
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