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Simplifying 8x2 + 20x + -24 = 2 Reorder the terms: -24 + 20x + 8x2 = 2 Solving -24 + 20x + 8x2 = 2 Solving for variable 'x'. Reorder the terms: -24 + -2 + 20x + 8x2 = 2 + -2 Combine like terms: -24 + -2 = -26 -26 + 20x + 8x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -26 + 20x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-13 + 10x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-13 + 10x + 4x2)' equal to zero and attempt to solve: Simplifying -13 + 10x + 4x2 = 0 Solving -13 + 10x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.25 + 2.5x + x2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + 2.5x + 3.25 + x2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + 2.5x + x2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + 2.5x + x2 = 0 + 3.25 2.5x + x2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 2.5x + x2 = 3.25 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 3.25 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 3.25 + 1.5625 Combine like terms: 3.25 + 1.5625 = 4.8125 1.5625 + 2.5x + x2 = 4.8125 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 4.8125 Calculate the square root of the right side: 2.193741097 Break this problem into two subproblems by setting (x + 1.25) equal to 2.193741097 and -2.193741097.Subproblem 1
x + 1.25 = 2.193741097 Simplifying x + 1.25 = 2.193741097 Reorder the terms: 1.25 + x = 2.193741097 Solving 1.25 + x = 2.193741097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 2.193741097 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 2.193741097 + -1.25 x = 2.193741097 + -1.25 Combine like terms: 2.193741097 + -1.25 = 0.943741097 x = 0.943741097 Simplifying x = 0.943741097Subproblem 2
x + 1.25 = -2.193741097 Simplifying x + 1.25 = -2.193741097 Reorder the terms: 1.25 + x = -2.193741097 Solving 1.25 + x = -2.193741097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -2.193741097 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -2.193741097 + -1.25 x = -2.193741097 + -1.25 Combine like terms: -2.193741097 + -1.25 = -3.443741097 x = -3.443741097 Simplifying x = -3.443741097Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.943741097, -3.443741097}Solution
x = {0.943741097, -3.443741097}
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