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Simplifying 350 + 2x(2x + 10) = 540 Reorder the terms: 350 + 2x(10 + 2x) = 540 350 + (10 * 2x + 2x * 2x) = 540 350 + (20x + 4x2) = 540 Solving 350 + 20x + 4x2 = 540 Solving for variable 'x'. Reorder the terms: 350 + -540 + 20x + 4x2 = 540 + -540 Combine like terms: 350 + -540 = -190 -190 + 20x + 4x2 = 540 + -540 Combine like terms: 540 + -540 = 0 -190 + 20x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-95 + 10x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-95 + 10x + 2x2)' equal to zero and attempt to solve: Simplifying -95 + 10x + 2x2 = 0 Solving -95 + 10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -47.5 + 5x + x2 = 0 Move the constant term to the right: Add '47.5' to each side of the equation. -47.5 + 5x + 47.5 + x2 = 0 + 47.5 Reorder the terms: -47.5 + 47.5 + 5x + x2 = 0 + 47.5 Combine like terms: -47.5 + 47.5 = 0.0 0.0 + 5x + x2 = 0 + 47.5 5x + x2 = 0 + 47.5 Combine like terms: 0 + 47.5 = 47.5 5x + x2 = 47.5 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 47.5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 47.5 + 6.25 Combine like terms: 47.5 + 6.25 = 53.75 6.25 + 5x + x2 = 53.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 53.75 Calculate the square root of the right side: 7.331439149 Break this problem into two subproblems by setting (x + 2.5) equal to 7.331439149 and -7.331439149.Subproblem 1
x + 2.5 = 7.331439149 Simplifying x + 2.5 = 7.331439149 Reorder the terms: 2.5 + x = 7.331439149 Solving 2.5 + x = 7.331439149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 7.331439149 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 7.331439149 + -2.5 x = 7.331439149 + -2.5 Combine like terms: 7.331439149 + -2.5 = 4.831439149 x = 4.831439149 Simplifying x = 4.831439149Subproblem 2
x + 2.5 = -7.331439149 Simplifying x + 2.5 = -7.331439149 Reorder the terms: 2.5 + x = -7.331439149 Solving 2.5 + x = -7.331439149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -7.331439149 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -7.331439149 + -2.5 x = -7.331439149 + -2.5 Combine like terms: -7.331439149 + -2.5 = -9.831439149 x = -9.831439149 Simplifying x = -9.831439149Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.831439149, -9.831439149}Solution
x = {4.831439149, -9.831439149}
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