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Simplifying 112x2 + -1x + -153 = 0 Reorder the terms: -153 + -1x + 112x2 = 0 Solving -153 + -1x + 112x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 112 the coefficient of the squared term: Divide each side by '112'. -1.366071429 + -0.008928571429x + x2 = 0 Move the constant term to the right: Add '1.366071429' to each side of the equation. -1.366071429 + -0.008928571429x + 1.366071429 + x2 = 0 + 1.366071429 Reorder the terms: -1.366071429 + 1.366071429 + -0.008928571429x + x2 = 0 + 1.366071429 Combine like terms: -1.366071429 + 1.366071429 = 0.000000000 0.000000000 + -0.008928571429x + x2 = 0 + 1.366071429 -0.008928571429x + x2 = 0 + 1.366071429 Combine like terms: 0 + 1.366071429 = 1.366071429 -0.008928571429x + x2 = 1.366071429 The x term is -0.008928571429x. Take half its coefficient (-0.004464285715). Square it (0.00001992984695) and add it to both sides. Add '0.00001992984695' to each side of the equation. -0.008928571429x + 0.00001992984695 + x2 = 1.366071429 + 0.00001992984695 Reorder the terms: 0.00001992984695 + -0.008928571429x + x2 = 1.366071429 + 0.00001992984695 Combine like terms: 1.366071429 + 0.00001992984695 = 1.36609135884695 0.00001992984695 + -0.008928571429x + x2 = 1.36609135884695 Factor a perfect square on the left side: (x + -0.004464285715)(x + -0.004464285715) = 1.36609135884695 Calculate the square root of the right side: 1.16879911 Break this problem into two subproblems by setting (x + -0.004464285715) equal to 1.16879911 and -1.16879911.Subproblem 1
x + -0.004464285715 = 1.16879911 Simplifying x + -0.004464285715 = 1.16879911 Reorder the terms: -0.004464285715 + x = 1.16879911 Solving -0.004464285715 + x = 1.16879911 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.004464285715' to each side of the equation. -0.004464285715 + 0.004464285715 + x = 1.16879911 + 0.004464285715 Combine like terms: -0.004464285715 + 0.004464285715 = 0.000000000000 0.000000000000 + x = 1.16879911 + 0.004464285715 x = 1.16879911 + 0.004464285715 Combine like terms: 1.16879911 + 0.004464285715 = 1.173263395715 x = 1.173263395715 Simplifying x = 1.173263395715Subproblem 2
x + -0.004464285715 = -1.16879911 Simplifying x + -0.004464285715 = -1.16879911 Reorder the terms: -0.004464285715 + x = -1.16879911 Solving -0.004464285715 + x = -1.16879911 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.004464285715' to each side of the equation. -0.004464285715 + 0.004464285715 + x = -1.16879911 + 0.004464285715 Combine like terms: -0.004464285715 + 0.004464285715 = 0.000000000000 0.000000000000 + x = -1.16879911 + 0.004464285715 x = -1.16879911 + 0.004464285715 Combine like terms: -1.16879911 + 0.004464285715 = -1.164334824285 x = -1.164334824285 Simplifying x = -1.164334824285Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.173263395715, -1.164334824285}
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