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Simplifying 2x2 + -28x + -98 = 0 Reorder the terms: -98 + -28x + 2x2 = 0 Solving -98 + -28x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-49 + -14x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-49 + -14x + x2)' equal to zero and attempt to solve: Simplifying -49 + -14x + x2 = 0 Solving -49 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + -14x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + -14x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -14x + x2 = 0 + 49 -14x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 -14x + x2 = 49 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 = 49 + 49 Reorder the terms: 49 + -14x + x2 = 49 + 49 Combine like terms: 49 + 49 = 98 49 + -14x + x2 = 98 Factor a perfect square on the left side: (x + -7)(x + -7) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (x + -7) equal to 9.899494937 and -9.899494937.Subproblem 1
x + -7 = 9.899494937 Simplifying x + -7 = 9.899494937 Reorder the terms: -7 + x = 9.899494937 Solving -7 + x = 9.899494937 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 = 9.899494937 + 7 Combine like terms: -7 + 7 = 0 0 + x = 9.899494937 + 7 x = 9.899494937 + 7 Combine like terms: 9.899494937 + 7 = 16.899494937 x = 16.899494937 Simplifying x = 16.899494937Subproblem 2
x + -7 = -9.899494937 Simplifying x + -7 = -9.899494937 Reorder the terms: -7 + x = -9.899494937 Solving -7 + x = -9.899494937 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 = -9.899494937 + 7 Combine like terms: -7 + 7 = 0 0 + x = -9.899494937 + 7 x = -9.899494937 + 7 Combine like terms: -9.899494937 + 7 = -2.899494937 x = -2.899494937 Simplifying x = -2.899494937Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.899494937, -2.899494937}Solution
x = {16.899494937, -2.899494937}
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