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Simplifying -4x2 + 24x + 40 = 4 Reorder the terms: 40 + 24x + -4x2 = 4 Solving 40 + 24x + -4x2 = 4 Solving for variable 'x'. Reorder the terms: 40 + -4 + 24x + -4x2 = 4 + -4 Combine like terms: 40 + -4 = 36 36 + 24x + -4x2 = 4 + -4 Combine like terms: 4 + -4 = 0 36 + 24x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(9 + 6x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(9 + 6x + -1x2)' equal to zero and attempt to solve: Simplifying 9 + 6x + -1x2 = 0 Solving 9 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9 + -6x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -6x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -6x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -6x + x2 = 0 + 9 -6x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -6x + x2 = 9 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 = 9 + 9 Reorder the terms: 9 + -6x + x2 = 9 + 9 Combine like terms: 9 + 9 = 18 9 + -6x + x2 = 18 Factor a perfect square on the left side: (x + -3)(x + -3) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (x + -3) equal to 4.242640687 and -4.242640687.Subproblem 1
x + -3 = 4.242640687 Simplifying x + -3 = 4.242640687 Reorder the terms: -3 + x = 4.242640687 Solving -3 + x = 4.242640687 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 = 4.242640687 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.242640687 + 3 x = 4.242640687 + 3 Combine like terms: 4.242640687 + 3 = 7.242640687 x = 7.242640687 Simplifying x = 7.242640687Subproblem 2
x + -3 = -4.242640687 Simplifying x + -3 = -4.242640687 Reorder the terms: -3 + x = -4.242640687 Solving -3 + x = -4.242640687 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 = -4.242640687 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.242640687 + 3 x = -4.242640687 + 3 Combine like terms: -4.242640687 + 3 = -1.242640687 x = -1.242640687 Simplifying x = -1.242640687Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.242640687, -1.242640687}Solution
x = {7.242640687, -1.242640687}
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