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Simplifying 2x2 + -28x + -58 = 0 Reorder the terms: -58 + -28x + 2x2 = 0 Solving -58 + -28x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-29 + -14x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-29 + -14x + x2)' equal to zero and attempt to solve: Simplifying -29 + -14x + x2 = 0 Solving -29 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + -14x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + -14x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -14x + x2 = 0 + 29 -14x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 -14x + x2 = 29 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 = 29 + 49 Reorder the terms: 49 + -14x + x2 = 29 + 49 Combine like terms: 29 + 49 = 78 49 + -14x + x2 = 78 Factor a perfect square on the left side: (x + -7)(x + -7) = 78 Calculate the square root of the right side: 8.831760866 Break this problem into two subproblems by setting (x + -7) equal to 8.831760866 and -8.831760866.Subproblem 1
x + -7 = 8.831760866 Simplifying x + -7 = 8.831760866 Reorder the terms: -7 + x = 8.831760866 Solving -7 + x = 8.831760866 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 = 8.831760866 + 7 Combine like terms: -7 + 7 = 0 0 + x = 8.831760866 + 7 x = 8.831760866 + 7 Combine like terms: 8.831760866 + 7 = 15.831760866 x = 15.831760866 Simplifying x = 15.831760866Subproblem 2
x + -7 = -8.831760866 Simplifying x + -7 = -8.831760866 Reorder the terms: -7 + x = -8.831760866 Solving -7 + x = -8.831760866 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 = -8.831760866 + 7 Combine like terms: -7 + 7 = 0 0 + x = -8.831760866 + 7 x = -8.831760866 + 7 Combine like terms: -8.831760866 + 7 = -1.831760866 x = -1.831760866 Simplifying x = -1.831760866Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.831760866, -1.831760866}Solution
x = {15.831760866, -1.831760866}
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