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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 + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(49 + -14x + -1x2)' equal to zero and attempt to solve: Simplifying 49 + -14x + -1x2 = 0 Solving 49 + -14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -49 + 14x + x2 = 0 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 = 2.899494937 x = 2.899494937 Simplifying x = 2.899494937Subproblem 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 = -16.899494937 x = -16.899494937 Simplifying x = -16.899494937Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.899494937, -16.899494937}Solution
x = {2.899494937, -16.899494937}
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