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Simplifying 2x2 + 8x = 70 Reorder the terms: 8x + 2x2 = 70 Solving 8x + 2x2 = 70 Solving for variable 'x'. Reorder the terms: -70 + 8x + 2x2 = 70 + -70 Combine like terms: 70 + -70 = 0 -70 + 8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-35 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-35 + 4x + x2)' equal to zero and attempt to solve: Simplifying -35 + 4x + x2 = 0 Solving -35 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + 4x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + 4x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 4x + x2 = 0 + 35 4x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 4x + x2 = 35 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 = 35 + 4 Reorder the terms: 4 + 4x + x2 = 35 + 4 Combine like terms: 35 + 4 = 39 4 + 4x + x2 = 39 Factor a perfect square on the left side: (x + 2)(x + 2) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (x + 2) equal to 6.244997998 and -6.244997998.Subproblem 1
x + 2 = 6.244997998 Simplifying x + 2 = 6.244997998 Reorder the terms: 2 + x = 6.244997998 Solving 2 + x = 6.244997998 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 = 6.244997998 + -2 Combine like terms: 2 + -2 = 0 0 + x = 6.244997998 + -2 x = 6.244997998 + -2 Combine like terms: 6.244997998 + -2 = 4.244997998 x = 4.244997998 Simplifying x = 4.244997998Subproblem 2
x + 2 = -6.244997998 Simplifying x + 2 = -6.244997998 Reorder the terms: 2 + x = -6.244997998 Solving 2 + x = -6.244997998 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 = -6.244997998 + -2 Combine like terms: 2 + -2 = 0 0 + x = -6.244997998 + -2 x = -6.244997998 + -2 Combine like terms: -6.244997998 + -2 = -8.244997998 x = -8.244997998 Simplifying x = -8.244997998Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.244997998, -8.244997998}Solution
x = {4.244997998, -8.244997998}
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