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Simplifying 24(36) = (2x + -4)(x + 6) Multiply 24 * 36 864 = (2x + -4)(x + 6) Reorder the terms: 864 = (-4 + 2x)(x + 6) Reorder the terms: 864 = (-4 + 2x)(6 + x) Multiply (-4 + 2x) * (6 + x) 864 = (-4(6 + x) + 2x * (6 + x)) 864 = ((6 * -4 + x * -4) + 2x * (6 + x)) 864 = ((-24 + -4x) + 2x * (6 + x)) 864 = (-24 + -4x + (6 * 2x + x * 2x)) 864 = (-24 + -4x + (12x + 2x2)) Combine like terms: -4x + 12x = 8x 864 = (-24 + 8x + 2x2) Solving 864 = -24 + 8x + 2x2 Solving for variable 'x'. Combine like terms: 864 + 24 = 888 888 + -8x + -2x2 = -24 + 8x + 2x2 + 24 + -8x + -2x2 Reorder the terms: 888 + -8x + -2x2 = -24 + 24 + 8x + -8x + 2x2 + -2x2 Combine like terms: -24 + 24 = 0 888 + -8x + -2x2 = 0 + 8x + -8x + 2x2 + -2x2 888 + -8x + -2x2 = 8x + -8x + 2x2 + -2x2 Combine like terms: 8x + -8x = 0 888 + -8x + -2x2 = 0 + 2x2 + -2x2 888 + -8x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 888 + -8x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(444 + -4x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(444 + -4x + -1x2)' equal to zero and attempt to solve: Simplifying 444 + -4x + -1x2 = 0 Solving 444 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -444 + 4x + x2 = 0 Move the constant term to the right: Add '444' to each side of the equation. -444 + 4x + 444 + x2 = 0 + 444 Reorder the terms: -444 + 444 + 4x + x2 = 0 + 444 Combine like terms: -444 + 444 = 0 0 + 4x + x2 = 0 + 444 4x + x2 = 0 + 444 Combine like terms: 0 + 444 = 444 4x + x2 = 444 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 444 + 4 Reorder the terms: 4 + 4x + x2 = 444 + 4 Combine like terms: 444 + 4 = 448 4 + 4x + x2 = 448 Factor a perfect square on the left side: (x + 2)(x + 2) = 448 Calculate the square root of the right side: 21.166010489 Break this problem into two subproblems by setting (x + 2) equal to 21.166010489 and -21.166010489.Subproblem 1
x + 2 = 21.166010489 Simplifying x + 2 = 21.166010489 Reorder the terms: 2 + x = 21.166010489 Solving 2 + x = 21.166010489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 21.166010489 + -2 Combine like terms: 2 + -2 = 0 0 + x = 21.166010489 + -2 x = 21.166010489 + -2 Combine like terms: 21.166010489 + -2 = 19.166010489 x = 19.166010489 Simplifying x = 19.166010489Subproblem 2
x + 2 = -21.166010489 Simplifying x + 2 = -21.166010489 Reorder the terms: 2 + x = -21.166010489 Solving 2 + x = -21.166010489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -21.166010489 + -2 Combine like terms: 2 + -2 = 0 0 + x = -21.166010489 + -2 x = -21.166010489 + -2 Combine like terms: -21.166010489 + -2 = -23.166010489 x = -23.166010489 Simplifying x = -23.166010489Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.166010489, -23.166010489}Solution
x = {19.166010489, -23.166010489}
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