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Simplifying 9 = 0.004x2 + -0.36x Reorder the terms: 9 = -0.36x + 0.004x2 Solving 9 = -0.36x + 0.004x2 Solving for variable 'x'. Reorder the terms: 9 + 0.36x + -0.004x2 = -0.36x + 0.36x + 0.004x2 + -0.004x2 Combine like terms: -0.36x + 0.36x = 0.00 9 + 0.36x + -0.004x2 = 0.00 + 0.004x2 + -0.004x2 9 + 0.36x + -0.004x2 = 0.004x2 + -0.004x2 Combine like terms: 0.004x2 + -0.004x2 = 0.000 9 + 0.36x + -0.004x2 = 0.000 Begin completing the square. Divide all terms by -0.004 the coefficient of the squared term: Divide each side by '-0.004'. -2250 + -90x + x2 = 0 Move the constant term to the right: Add '2250' to each side of the equation. -2250 + -90x + 2250 + x2 = 0 + 2250 Reorder the terms: -2250 + 2250 + -90x + x2 = 0 + 2250 Combine like terms: -2250 + 2250 = 0 0 + -90x + x2 = 0 + 2250 -90x + x2 = 0 + 2250 Combine like terms: 0 + 2250 = 2250 -90x + x2 = 2250 The x term is -90x. Take half its coefficient (-45). Square it (2025) and add it to both sides. Add '2025' to each side of the equation. -90x + 2025 + x2 = 2250 + 2025 Reorder the terms: 2025 + -90x + x2 = 2250 + 2025 Combine like terms: 2250 + 2025 = 4275 2025 + -90x + x2 = 4275 Factor a perfect square on the left side: (x + -45)(x + -45) = 4275 Calculate the square root of the right side: 65.383484153 Break this problem into two subproblems by setting (x + -45) equal to 65.383484153 and -65.383484153.Subproblem 1
x + -45 = 65.383484153 Simplifying x + -45 = 65.383484153 Reorder the terms: -45 + x = 65.383484153 Solving -45 + x = 65.383484153 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + x = 65.383484153 + 45 Combine like terms: -45 + 45 = 0 0 + x = 65.383484153 + 45 x = 65.383484153 + 45 Combine like terms: 65.383484153 + 45 = 110.383484153 x = 110.383484153 Simplifying x = 110.383484153Subproblem 2
x + -45 = -65.383484153 Simplifying x + -45 = -65.383484153 Reorder the terms: -45 + x = -65.383484153 Solving -45 + x = -65.383484153 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + x = -65.383484153 + 45 Combine like terms: -45 + 45 = 0 0 + x = -65.383484153 + 45 x = -65.383484153 + 45 Combine like terms: -65.383484153 + 45 = -20.383484153 x = -20.383484153 Simplifying x = -20.383484153Solution
The solution to the problem is based on the solutions from the subproblems. x = {110.383484153, -20.383484153}
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