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Simplifying 2x2 + -28x + 66 = -2 Reorder the terms: 66 + -28x + 2x2 = -2 Solving 66 + -28x + 2x2 = -2 Solving for variable 'x'. Reorder the terms: 66 + 2 + -28x + 2x2 = -2 + 2 Combine like terms: 66 + 2 = 68 68 + -28x + 2x2 = -2 + 2 Combine like terms: -2 + 2 = 0 68 + -28x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(34 + -14x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(34 + -14x + x2)' equal to zero and attempt to solve: Simplifying 34 + -14x + x2 = 0 Solving 34 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-34' to each side of the equation. 34 + -14x + -34 + x2 = 0 + -34 Reorder the terms: 34 + -34 + -14x + x2 = 0 + -34 Combine like terms: 34 + -34 = 0 0 + -14x + x2 = 0 + -34 -14x + x2 = 0 + -34 Combine like terms: 0 + -34 = -34 -14x + x2 = -34 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -34 + 49 Reorder the terms: 49 + -14x + x2 = -34 + 49 Combine like terms: -34 + 49 = 15 49 + -14x + x2 = 15 Factor a perfect square on the left side: (x + -7)(x + -7) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x + -7) equal to 3.872983346 and -3.872983346.Subproblem 1
x + -7 = 3.872983346 Simplifying x + -7 = 3.872983346 Reorder the terms: -7 + x = 3.872983346 Solving -7 + x = 3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 3.872983346 + 7 Combine like terms: -7 + 7 = 0 0 + x = 3.872983346 + 7 x = 3.872983346 + 7 Combine like terms: 3.872983346 + 7 = 10.872983346 x = 10.872983346 Simplifying x = 10.872983346Subproblem 2
x + -7 = -3.872983346 Simplifying x + -7 = -3.872983346 Reorder the terms: -7 + x = -3.872983346 Solving -7 + x = -3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -3.872983346 + 7 Combine like terms: -7 + 7 = 0 0 + x = -3.872983346 + 7 x = -3.872983346 + 7 Combine like terms: -3.872983346 + 7 = 3.127016654 x = 3.127016654 Simplifying x = 3.127016654Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.872983346, 3.127016654}Solution
x = {10.872983346, 3.127016654}
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