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Simplifying 266 = 2x2 + 70x Reorder the terms: 266 = 70x + 2x2 Solving 266 = 70x + 2x2 Solving for variable 'x'. Reorder the terms: 266 + -70x + -2x2 = 70x + -70x + 2x2 + -2x2 Combine like terms: 70x + -70x = 0 266 + -70x + -2x2 = 0 + 2x2 + -2x2 266 + -70x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 266 + -70x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(133 + -35x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(133 + -35x + -1x2)' equal to zero and attempt to solve: Simplifying 133 + -35x + -1x2 = 0 Solving 133 + -35x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -133 + 35x + x2 = 0 Move the constant term to the right: Add '133' to each side of the equation. -133 + 35x + 133 + x2 = 0 + 133 Reorder the terms: -133 + 133 + 35x + x2 = 0 + 133 Combine like terms: -133 + 133 = 0 0 + 35x + x2 = 0 + 133 35x + x2 = 0 + 133 Combine like terms: 0 + 133 = 133 35x + x2 = 133 The x term is 35x. Take half its coefficient (17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. 35x + 306.25 + x2 = 133 + 306.25 Reorder the terms: 306.25 + 35x + x2 = 133 + 306.25 Combine like terms: 133 + 306.25 = 439.25 306.25 + 35x + x2 = 439.25 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = 439.25 Calculate the square root of the right side: 20.958291915 Break this problem into two subproblems by setting (x + 17.5) equal to 20.958291915 and -20.958291915.Subproblem 1
x + 17.5 = 20.958291915 Simplifying x + 17.5 = 20.958291915 Reorder the terms: 17.5 + x = 20.958291915 Solving 17.5 + x = 20.958291915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = 20.958291915 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 20.958291915 + -17.5 x = 20.958291915 + -17.5 Combine like terms: 20.958291915 + -17.5 = 3.458291915 x = 3.458291915 Simplifying x = 3.458291915Subproblem 2
x + 17.5 = -20.958291915 Simplifying x + 17.5 = -20.958291915 Reorder the terms: 17.5 + x = -20.958291915 Solving 17.5 + x = -20.958291915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = -20.958291915 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -20.958291915 + -17.5 x = -20.958291915 + -17.5 Combine like terms: -20.958291915 + -17.5 = -38.458291915 x = -38.458291915 Simplifying x = -38.458291915Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.458291915, -38.458291915}Solution
x = {3.458291915, -38.458291915}
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