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Simplifying 0.15x2 + -46x + 1100 = 0 Reorder the terms: 1100 + -46x + 0.15x2 = 0 Solving 1100 + -46x + 0.15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.15 the coefficient of the squared term: Divide each side by '0.15'. 7333.333333 + -306.6666667x + x2 = 0 Move the constant term to the right: Add '-7333.333333' to each side of the equation. 7333.333333 + -306.6666667x + -7333.333333 + x2 = 0 + -7333.333333 Reorder the terms: 7333.333333 + -7333.333333 + -306.6666667x + x2 = 0 + -7333.333333 Combine like terms: 7333.333333 + -7333.333333 = 0.000000 0.000000 + -306.6666667x + x2 = 0 + -7333.333333 -306.6666667x + x2 = 0 + -7333.333333 Combine like terms: 0 + -7333.333333 = -7333.333333 -306.6666667x + x2 = -7333.333333 The x term is -306.6666667x. Take half its coefficient (-153.3333334). Square it (23511.11113) and add it to both sides. Add '23511.11113' to each side of the equation. -306.6666667x + 23511.11113 + x2 = -7333.333333 + 23511.11113 Reorder the terms: 23511.11113 + -306.6666667x + x2 = -7333.333333 + 23511.11113 Combine like terms: -7333.333333 + 23511.11113 = 16177.777797 23511.11113 + -306.6666667x + x2 = 16177.777797 Factor a perfect square on the left side: (x + -153.3333334)(x + -153.3333334) = 16177.777797 Calculate the square root of the right side: 127.191893598 Break this problem into two subproblems by setting (x + -153.3333334) equal to 127.191893598 and -127.191893598.Subproblem 1
x + -153.3333334 = 127.191893598 Simplifying x + -153.3333334 = 127.191893598 Reorder the terms: -153.3333334 + x = 127.191893598 Solving -153.3333334 + x = 127.191893598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '153.3333334' to each side of the equation. -153.3333334 + 153.3333334 + x = 127.191893598 + 153.3333334 Combine like terms: -153.3333334 + 153.3333334 = 0.0000000 0.0000000 + x = 127.191893598 + 153.3333334 x = 127.191893598 + 153.3333334 Combine like terms: 127.191893598 + 153.3333334 = 280.525226998 x = 280.525226998 Simplifying x = 280.525226998Subproblem 2
x + -153.3333334 = -127.191893598 Simplifying x + -153.3333334 = -127.191893598 Reorder the terms: -153.3333334 + x = -127.191893598 Solving -153.3333334 + x = -127.191893598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '153.3333334' to each side of the equation. -153.3333334 + 153.3333334 + x = -127.191893598 + 153.3333334 Combine like terms: -153.3333334 + 153.3333334 = 0.0000000 0.0000000 + x = -127.191893598 + 153.3333334 x = -127.191893598 + 153.3333334 Combine like terms: -127.191893598 + 153.3333334 = 26.141439802 x = 26.141439802 Simplifying x = 26.141439802Solution
The solution to the problem is based on the solutions from the subproblems. x = {280.525226998, 26.141439802}
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