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Simplifying 0 = -0.000012x2 + 0.01x + 114 Reorder the terms: 0 = 114 + 0.01x + -0.000012x2 Solving 0 = 114 + 0.01x + -0.000012x2 Solving for variable 'x'. Combine like terms: 0 + -114 = -114 -114 + -0.01x + 0.000012x2 = 114 + 0.01x + -0.000012x2 + -114 + -0.01x + 0.000012x2 Reorder the terms: -114 + -0.01x + 0.000012x2 = 114 + -114 + 0.01x + -0.01x + -0.000012x2 + 0.000012x2 Combine like terms: 114 + -114 = 0 -114 + -0.01x + 0.000012x2 = 0 + 0.01x + -0.01x + -0.000012x2 + 0.000012x2 -114 + -0.01x + 0.000012x2 = 0.01x + -0.01x + -0.000012x2 + 0.000012x2 Combine like terms: 0.01x + -0.01x = 0.00 -114 + -0.01x + 0.000012x2 = 0.00 + -0.000012x2 + 0.000012x2 -114 + -0.01x + 0.000012x2 = -0.000012x2 + 0.000012x2 Combine like terms: -0.000012x2 + 0.000012x2 = 0.000000 -114 + -0.01x + 0.000012x2 = 0.000000 Begin completing the square. Divide all terms by 0.000012 the coefficient of the squared term: Divide each side by '0.000012'. -9500000 + -833.3333333x + x2 = 0 Move the constant term to the right: Add '9500000' to each side of the equation. -9500000 + -833.3333333x + 9500000 + x2 = 0 + 9500000 Reorder the terms: -9500000 + 9500000 + -833.3333333x + x2 = 0 + 9500000 Combine like terms: -9500000 + 9500000 = 0 0 + -833.3333333x + x2 = 0 + 9500000 -833.3333333x + x2 = 0 + 9500000 Combine like terms: 0 + 9500000 = 9500000 -833.3333333x + x2 = 9500000 The x term is -833.3333333x. Take half its coefficient (-416.6666667). Square it (173611.1111) and add it to both sides. Add '173611.1111' to each side of the equation. -833.3333333x + 173611.1111 + x2 = 9500000 + 173611.1111 Reorder the terms: 173611.1111 + -833.3333333x + x2 = 9500000 + 173611.1111 Combine like terms: 9500000 + 173611.1111 = 9673611.1111 173611.1111 + -833.3333333x + x2 = 9673611.1111 Factor a perfect square on the left side: (x + -416.6666667)(x + -416.6666667) = 9673611.1111 Calculate the square root of the right side: 3110.242934418 Break this problem into two subproblems by setting (x + -416.6666667) equal to 3110.242934418 and -3110.242934418.Subproblem 1
x + -416.6666667 = 3110.242934418 Simplifying x + -416.6666667 = 3110.242934418 Reorder the terms: -416.6666667 + x = 3110.242934418 Solving -416.6666667 + x = 3110.242934418 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '416.6666667' to each side of the equation. -416.6666667 + 416.6666667 + x = 3110.242934418 + 416.6666667 Combine like terms: -416.6666667 + 416.6666667 = 0.0000000 0.0000000 + x = 3110.242934418 + 416.6666667 x = 3110.242934418 + 416.6666667 Combine like terms: 3110.242934418 + 416.6666667 = 3526.909601118 x = 3526.909601118 Simplifying x = 3526.909601118Subproblem 2
x + -416.6666667 = -3110.242934418 Simplifying x + -416.6666667 = -3110.242934418 Reorder the terms: -416.6666667 + x = -3110.242934418 Solving -416.6666667 + x = -3110.242934418 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '416.6666667' to each side of the equation. -416.6666667 + 416.6666667 + x = -3110.242934418 + 416.6666667 Combine like terms: -416.6666667 + 416.6666667 = 0.0000000 0.0000000 + x = -3110.242934418 + 416.6666667 x = -3110.242934418 + 416.6666667 Combine like terms: -3110.242934418 + 416.6666667 = -2693.576267718 x = -2693.576267718 Simplifying x = -2693.576267718Solution
The solution to the problem is based on the solutions from the subproblems. x = {3526.909601118, -2693.576267718}
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