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Simplifying 8x2 + -34x = -24 Reorder the terms: -34x + 8x2 = -24 Solving -34x + 8x2 = -24 Solving for variable 'x'. Reorder the terms: 24 + -34x + 8x2 = -24 + 24 Combine like terms: -24 + 24 = 0 24 + -34x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(12 + -17x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + -17x + 4x2)' equal to zero and attempt to solve: Simplifying 12 + -17x + 4x2 = 0 Solving 12 + -17x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3 + -4.25x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -4.25x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -4.25x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4.25x + x2 = 0 + -3 -4.25x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -4.25x + x2 = -3 The x term is -4.25x. Take half its coefficient (-2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. -4.25x + 4.515625 + x2 = -3 + 4.515625 Reorder the terms: 4.515625 + -4.25x + x2 = -3 + 4.515625 Combine like terms: -3 + 4.515625 = 1.515625 4.515625 + -4.25x + x2 = 1.515625 Factor a perfect square on the left side: (x + -2.125)(x + -2.125) = 1.515625 Calculate the square root of the right side: 1.231107225 Break this problem into two subproblems by setting (x + -2.125) equal to 1.231107225 and -1.231107225.Subproblem 1
x + -2.125 = 1.231107225 Simplifying x + -2.125 = 1.231107225 Reorder the terms: -2.125 + x = 1.231107225 Solving -2.125 + x = 1.231107225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = 1.231107225 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = 1.231107225 + 2.125 x = 1.231107225 + 2.125 Combine like terms: 1.231107225 + 2.125 = 3.356107225 x = 3.356107225 Simplifying x = 3.356107225Subproblem 2
x + -2.125 = -1.231107225 Simplifying x + -2.125 = -1.231107225 Reorder the terms: -2.125 + x = -1.231107225 Solving -2.125 + x = -1.231107225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = -1.231107225 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = -1.231107225 + 2.125 x = -1.231107225 + 2.125 Combine like terms: -1.231107225 + 2.125 = 0.893892775 x = 0.893892775 Simplifying x = 0.893892775Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.356107225, 0.893892775}Solution
x = {3.356107225, 0.893892775}
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