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Simplifying 4x2 + -15x + -11 = 0 Reorder the terms: -11 + -15x + 4x2 = 0 Solving -11 + -15x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.75 + -3.75x + x2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + -3.75x + 2.75 + x2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + -3.75x + x2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + -3.75x + x2 = 0 + 2.75 -3.75x + x2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 -3.75x + x2 = 2.75 The x term is -3.75x. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75x + 3.515625 + x2 = 2.75 + 3.515625 Reorder the terms: 3.515625 + -3.75x + x2 = 2.75 + 3.515625 Combine like terms: 2.75 + 3.515625 = 6.265625 3.515625 + -3.75x + x2 = 6.265625 Factor a perfect square on the left side: (x + -1.875)(x + -1.875) = 6.265625 Calculate the square root of the right side: 2.503123049 Break this problem into two subproblems by setting (x + -1.875) equal to 2.503123049 and -2.503123049.Subproblem 1
x + -1.875 = 2.503123049 Simplifying x + -1.875 = 2.503123049 Reorder the terms: -1.875 + x = 2.503123049 Solving -1.875 + x = 2.503123049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = 2.503123049 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 2.503123049 + 1.875 x = 2.503123049 + 1.875 Combine like terms: 2.503123049 + 1.875 = 4.378123049 x = 4.378123049 Simplifying x = 4.378123049Subproblem 2
x + -1.875 = -2.503123049 Simplifying x + -1.875 = -2.503123049 Reorder the terms: -1.875 + x = -2.503123049 Solving -1.875 + x = -2.503123049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = -2.503123049 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -2.503123049 + 1.875 x = -2.503123049 + 1.875 Combine like terms: -2.503123049 + 1.875 = -0.628123049 x = -0.628123049 Simplifying x = -0.628123049Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.378123049, -0.628123049}
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