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Simplifying 8x2 + 24x = 10 Reorder the terms: 24x + 8x2 = 10 Solving 24x + 8x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + 24x + 8x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 24x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 12x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 12x + 4x2)' equal to zero and attempt to solve: Simplifying -5 + 12x + 4x2 = 0 Solving -5 + 12x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + 3x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 3x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 3x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 3x + x2 = 0 + 1.25 3x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 3x + x2 = 1.25 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 1.25 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 1.25 + 2.25 Combine like terms: 1.25 + 2.25 = 3.5 2.25 + 3x + x2 = 3.5 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 3.5 Calculate the square root of the right side: 1.870828693 Break this problem into two subproblems by setting (x + 1.5) equal to 1.870828693 and -1.870828693.Subproblem 1
x + 1.5 = 1.870828693 Simplifying x + 1.5 = 1.870828693 Reorder the terms: 1.5 + x = 1.870828693 Solving 1.5 + x = 1.870828693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.870828693 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.870828693 + -1.5 x = 1.870828693 + -1.5 Combine like terms: 1.870828693 + -1.5 = 0.370828693 x = 0.370828693 Simplifying x = 0.370828693Subproblem 2
x + 1.5 = -1.870828693 Simplifying x + 1.5 = -1.870828693 Reorder the terms: 1.5 + x = -1.870828693 Solving 1.5 + x = -1.870828693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.870828693 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.870828693 + -1.5 x = -1.870828693 + -1.5 Combine like terms: -1.870828693 + -1.5 = -3.370828693 x = -3.370828693 Simplifying x = -3.370828693Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.370828693, -3.370828693}Solution
x = {0.370828693, -3.370828693}
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