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Simplifying 2x2 + 6x = 136 Reorder the terms: 6x + 2x2 = 136 Solving 6x + 2x2 = 136 Solving for variable 'x'. Reorder the terms: -136 + 6x + 2x2 = 136 + -136 Combine like terms: 136 + -136 = 0 -136 + 6x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-68 + 3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-68 + 3x + x2)' equal to zero and attempt to solve: Simplifying -68 + 3x + x2 = 0 Solving -68 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '68' to each side of the equation. -68 + 3x + 68 + x2 = 0 + 68 Reorder the terms: -68 + 68 + 3x + x2 = 0 + 68 Combine like terms: -68 + 68 = 0 0 + 3x + x2 = 0 + 68 3x + x2 = 0 + 68 Combine like terms: 0 + 68 = 68 3x + x2 = 68 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 = 68 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 68 + 2.25 Combine like terms: 68 + 2.25 = 70.25 2.25 + 3x + x2 = 70.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 70.25 Calculate the square root of the right side: 8.381527307 Break this problem into two subproblems by setting (x + 1.5) equal to 8.381527307 and -8.381527307.Subproblem 1
x + 1.5 = 8.381527307 Simplifying x + 1.5 = 8.381527307 Reorder the terms: 1.5 + x = 8.381527307 Solving 1.5 + x = 8.381527307 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 = 8.381527307 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 8.381527307 + -1.5 x = 8.381527307 + -1.5 Combine like terms: 8.381527307 + -1.5 = 6.881527307 x = 6.881527307 Simplifying x = 6.881527307Subproblem 2
x + 1.5 = -8.381527307 Simplifying x + 1.5 = -8.381527307 Reorder the terms: 1.5 + x = -8.381527307 Solving 1.5 + x = -8.381527307 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 = -8.381527307 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -8.381527307 + -1.5 x = -8.381527307 + -1.5 Combine like terms: -8.381527307 + -1.5 = -9.881527307 x = -9.881527307 Simplifying x = -9.881527307Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.881527307, -9.881527307}Solution
x = {6.881527307, -9.881527307}
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