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Simplifying 196 = 100 + 20x + x2 + 16 + 8x + x2 Reorder the terms: 196 = 100 + 16 + 20x + 8x + x2 + x2 Combine like terms: 100 + 16 = 116 196 = 116 + 20x + 8x + x2 + x2 Combine like terms: 20x + 8x = 28x 196 = 116 + 28x + x2 + x2 Combine like terms: x2 + x2 = 2x2 196 = 116 + 28x + 2x2 Solving 196 = 116 + 28x + 2x2 Solving for variable 'x'. Combine like terms: 196 + -116 = 80 80 + -28x + -2x2 = 116 + 28x + 2x2 + -116 + -28x + -2x2 Reorder the terms: 80 + -28x + -2x2 = 116 + -116 + 28x + -28x + 2x2 + -2x2 Combine like terms: 116 + -116 = 0 80 + -28x + -2x2 = 0 + 28x + -28x + 2x2 + -2x2 80 + -28x + -2x2 = 28x + -28x + 2x2 + -2x2 Combine like terms: 28x + -28x = 0 80 + -28x + -2x2 = 0 + 2x2 + -2x2 80 + -28x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 80 + -28x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(40 + -14x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(40 + -14x + -1x2)' equal to zero and attempt to solve: Simplifying 40 + -14x + -1x2 = 0 Solving 40 + -14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -40 + 14x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + 14x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + 14x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 14x + x2 = 0 + 40 14x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 14x + x2 = 40 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 = 40 + 49 Reorder the terms: 49 + 14x + x2 = 40 + 49 Combine like terms: 40 + 49 = 89 49 + 14x + x2 = 89 Factor a perfect square on the left side: (x + 7)(x + 7) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (x + 7) equal to 9.433981132 and -9.433981132.Subproblem 1
x + 7 = 9.433981132 Simplifying x + 7 = 9.433981132 Reorder the terms: 7 + x = 9.433981132 Solving 7 + x = 9.433981132 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 = 9.433981132 + -7 Combine like terms: 7 + -7 = 0 0 + x = 9.433981132 + -7 x = 9.433981132 + -7 Combine like terms: 9.433981132 + -7 = 2.433981132 x = 2.433981132 Simplifying x = 2.433981132Subproblem 2
x + 7 = -9.433981132 Simplifying x + 7 = -9.433981132 Reorder the terms: 7 + x = -9.433981132 Solving 7 + x = -9.433981132 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 = -9.433981132 + -7 Combine like terms: 7 + -7 = 0 0 + x = -9.433981132 + -7 x = -9.433981132 + -7 Combine like terms: -9.433981132 + -7 = -16.433981132 x = -16.433981132 Simplifying x = -16.433981132Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.433981132, -16.433981132}Solution
x = {2.433981132, -16.433981132}
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