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Simplifying 0.007x2 + 0.02x = 150 Reorder the terms: 0.02x + 0.007x2 = 150 Solving 0.02x + 0.007x2 = 150 Solving for variable 'x'. Reorder the terms: -150 + 0.02x + 0.007x2 = 150 + -150 Combine like terms: 150 + -150 = 0 -150 + 0.02x + 0.007x2 = 0 Begin completing the square. Divide all terms by 0.007 the coefficient of the squared term: Divide each side by '0.007'. -21428.57143 + 2.857142857x + x2 = 0 Move the constant term to the right: Add '21428.57143' to each side of the equation. -21428.57143 + 2.857142857x + 21428.57143 + x2 = 0 + 21428.57143 Reorder the terms: -21428.57143 + 21428.57143 + 2.857142857x + x2 = 0 + 21428.57143 Combine like terms: -21428.57143 + 21428.57143 = 0.00000 0.00000 + 2.857142857x + x2 = 0 + 21428.57143 2.857142857x + x2 = 0 + 21428.57143 Combine like terms: 0 + 21428.57143 = 21428.57143 2.857142857x + x2 = 21428.57143 The x term is 2.857142857x. Take half its coefficient (1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. 2.857142857x + 2.040816328 + x2 = 21428.57143 + 2.040816328 Reorder the terms: 2.040816328 + 2.857142857x + x2 = 21428.57143 + 2.040816328 Combine like terms: 21428.57143 + 2.040816328 = 21430.612246328 2.040816328 + 2.857142857x + x2 = 21430.612246328 Factor a perfect square on the left side: (x + 1.428571429)(x + 1.428571429) = 21430.612246328 Calculate the square root of the right side: 146.391981496 Break this problem into two subproblems by setting (x + 1.428571429) equal to 146.391981496 and -146.391981496.Subproblem 1
x + 1.428571429 = 146.391981496 Simplifying x + 1.428571429 = 146.391981496 Reorder the terms: 1.428571429 + x = 146.391981496 Solving 1.428571429 + x = 146.391981496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.428571429' to each side of the equation. 1.428571429 + -1.428571429 + x = 146.391981496 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + x = 146.391981496 + -1.428571429 x = 146.391981496 + -1.428571429 Combine like terms: 146.391981496 + -1.428571429 = 144.963410067 x = 144.963410067 Simplifying x = 144.963410067Subproblem 2
x + 1.428571429 = -146.391981496 Simplifying x + 1.428571429 = -146.391981496 Reorder the terms: 1.428571429 + x = -146.391981496 Solving 1.428571429 + x = -146.391981496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.428571429' to each side of the equation. 1.428571429 + -1.428571429 + x = -146.391981496 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + x = -146.391981496 + -1.428571429 x = -146.391981496 + -1.428571429 Combine like terms: -146.391981496 + -1.428571429 = -147.820552925 x = -147.820552925 Simplifying x = -147.820552925Solution
The solution to the problem is based on the solutions from the subproblems. x = {144.963410067, -147.820552925}
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