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Simplifying 2x2 + -47x + 155 = 0 Reorder the terms: 155 + -47x + 2x2 = 0 Solving 155 + -47x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 77.5 + -23.5x + x2 = 0 Move the constant term to the right: Add '-77.5' to each side of the equation. 77.5 + -23.5x + -77.5 + x2 = 0 + -77.5 Reorder the terms: 77.5 + -77.5 + -23.5x + x2 = 0 + -77.5 Combine like terms: 77.5 + -77.5 = 0.0 0.0 + -23.5x + x2 = 0 + -77.5 -23.5x + x2 = 0 + -77.5 Combine like terms: 0 + -77.5 = -77.5 -23.5x + x2 = -77.5 The x term is -23.5x. Take half its coefficient (-11.75). Square it (138.0625) and add it to both sides. Add '138.0625' to each side of the equation. -23.5x + 138.0625 + x2 = -77.5 + 138.0625 Reorder the terms: 138.0625 + -23.5x + x2 = -77.5 + 138.0625 Combine like terms: -77.5 + 138.0625 = 60.5625 138.0625 + -23.5x + x2 = 60.5625 Factor a perfect square on the left side: (x + -11.75)(x + -11.75) = 60.5625 Calculate the square root of the right side: 7.782191208 Break this problem into two subproblems by setting (x + -11.75) equal to 7.782191208 and -7.782191208.Subproblem 1
x + -11.75 = 7.782191208 Simplifying x + -11.75 = 7.782191208 Reorder the terms: -11.75 + x = 7.782191208 Solving -11.75 + x = 7.782191208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.75' to each side of the equation. -11.75 + 11.75 + x = 7.782191208 + 11.75 Combine like terms: -11.75 + 11.75 = 0.00 0.00 + x = 7.782191208 + 11.75 x = 7.782191208 + 11.75 Combine like terms: 7.782191208 + 11.75 = 19.532191208 x = 19.532191208 Simplifying x = 19.532191208Subproblem 2
x + -11.75 = -7.782191208 Simplifying x + -11.75 = -7.782191208 Reorder the terms: -11.75 + x = -7.782191208 Solving -11.75 + x = -7.782191208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.75' to each side of the equation. -11.75 + 11.75 + x = -7.782191208 + 11.75 Combine like terms: -11.75 + 11.75 = 0.00 0.00 + x = -7.782191208 + 11.75 x = -7.782191208 + 11.75 Combine like terms: -7.782191208 + 11.75 = 3.967808792 x = 3.967808792 Simplifying x = 3.967808792Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.532191208, 3.967808792}
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