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Simplifying -8 = 3x2 + 24x Reorder the terms: -8 = 24x + 3x2 Solving -8 = 24x + 3x2 Solving for variable 'x'. Reorder the terms: -8 + -24x + -3x2 = 24x + -24x + 3x2 + -3x2 Combine like terms: 24x + -24x = 0 -8 + -24x + -3x2 = 0 + 3x2 + -3x2 -8 + -24x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -8 + -24x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 24x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 24x + 3x2)' equal to zero and attempt to solve: Simplifying 8 + 24x + 3x2 = 0 Solving 8 + 24x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.666666667 + 8x + x2 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + 8x + -2.666666667 + x2 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + 8x + x2 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + 8x + x2 = 0 + -2.666666667 8x + x2 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 8x + x2 = -2.666666667 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -2.666666667 + 16 Reorder the terms: 16 + 8x + x2 = -2.666666667 + 16 Combine like terms: -2.666666667 + 16 = 13.333333333 16 + 8x + x2 = 13.333333333 Factor a perfect square on the left side: (x + 4)(x + 4) = 13.333333333 Calculate the square root of the right side: 3.651483717 Break this problem into two subproblems by setting (x + 4) equal to 3.651483717 and -3.651483717.Subproblem 1
x + 4 = 3.651483717 Simplifying x + 4 = 3.651483717 Reorder the terms: 4 + x = 3.651483717 Solving 4 + x = 3.651483717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 3.651483717 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.651483717 + -4 x = 3.651483717 + -4 Combine like terms: 3.651483717 + -4 = -0.348516283 x = -0.348516283 Simplifying x = -0.348516283Subproblem 2
x + 4 = -3.651483717 Simplifying x + 4 = -3.651483717 Reorder the terms: 4 + x = -3.651483717 Solving 4 + x = -3.651483717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -3.651483717 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.651483717 + -4 x = -3.651483717 + -4 Combine like terms: -3.651483717 + -4 = -7.651483717 x = -7.651483717 Simplifying x = -7.651483717Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.348516283, -7.651483717}Solution
x = {-0.348516283, -7.651483717}
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