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Simplifying 165x2 + -14.93x + -15.6765 = 0 Reorder the terms: -15.6765 + -14.93x + 165x2 = 0 Solving -15.6765 + -14.93x + 165x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 165 the coefficient of the squared term: Divide each side by '165'. -0.09500909091 + -0.09048484848x + x2 = 0 Move the constant term to the right: Add '0.09500909091' to each side of the equation. -0.09500909091 + -0.09048484848x + 0.09500909091 + x2 = 0 + 0.09500909091 Reorder the terms: -0.09500909091 + 0.09500909091 + -0.09048484848x + x2 = 0 + 0.09500909091 Combine like terms: -0.09500909091 + 0.09500909091 = 0.00000000000 0.00000000000 + -0.09048484848x + x2 = 0 + 0.09500909091 -0.09048484848x + x2 = 0 + 0.09500909091 Combine like terms: 0 + 0.09500909091 = 0.09500909091 -0.09048484848x + x2 = 0.09500909091 The x term is -0.09048484848x. Take half its coefficient (-0.04524242424). Square it (0.002046876951) and add it to both sides. Add '0.002046876951' to each side of the equation. -0.09048484848x + 0.002046876951 + x2 = 0.09500909091 + 0.002046876951 Reorder the terms: 0.002046876951 + -0.09048484848x + x2 = 0.09500909091 + 0.002046876951 Combine like terms: 0.09500909091 + 0.002046876951 = 0.097055967861 0.002046876951 + -0.09048484848x + x2 = 0.097055967861 Factor a perfect square on the left side: (x + -0.04524242424)(x + -0.04524242424) = 0.097055967861 Calculate the square root of the right side: 0.311538068 Break this problem into two subproblems by setting (x + -0.04524242424) equal to 0.311538068 and -0.311538068.Subproblem 1
x + -0.04524242424 = 0.311538068 Simplifying x + -0.04524242424 = 0.311538068 Reorder the terms: -0.04524242424 + x = 0.311538068 Solving -0.04524242424 + x = 0.311538068 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04524242424' to each side of the equation. -0.04524242424 + 0.04524242424 + x = 0.311538068 + 0.04524242424 Combine like terms: -0.04524242424 + 0.04524242424 = 0.00000000000 0.00000000000 + x = 0.311538068 + 0.04524242424 x = 0.311538068 + 0.04524242424 Combine like terms: 0.311538068 + 0.04524242424 = 0.35678049224 x = 0.35678049224 Simplifying x = 0.35678049224Subproblem 2
x + -0.04524242424 = -0.311538068 Simplifying x + -0.04524242424 = -0.311538068 Reorder the terms: -0.04524242424 + x = -0.311538068 Solving -0.04524242424 + x = -0.311538068 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04524242424' to each side of the equation. -0.04524242424 + 0.04524242424 + x = -0.311538068 + 0.04524242424 Combine like terms: -0.04524242424 + 0.04524242424 = 0.00000000000 0.00000000000 + x = -0.311538068 + 0.04524242424 x = -0.311538068 + 0.04524242424 Combine like terms: -0.311538068 + 0.04524242424 = -0.26629564376 x = -0.26629564376 Simplifying x = -0.26629564376Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.35678049224, -0.26629564376}
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