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Simplifying 25 = -0.01x2 + 0.9x + 10 Reorder the terms: 25 = 10 + 0.9x + -0.01x2 Solving 25 = 10 + 0.9x + -0.01x2 Solving for variable 'x'. Combine like terms: 25 + -10 = 15 15 + -0.9x + 0.01x2 = 10 + 0.9x + -0.01x2 + -10 + -0.9x + 0.01x2 Reorder the terms: 15 + -0.9x + 0.01x2 = 10 + -10 + 0.9x + -0.9x + -0.01x2 + 0.01x2 Combine like terms: 10 + -10 = 0 15 + -0.9x + 0.01x2 = 0 + 0.9x + -0.9x + -0.01x2 + 0.01x2 15 + -0.9x + 0.01x2 = 0.9x + -0.9x + -0.01x2 + 0.01x2 Combine like terms: 0.9x + -0.9x = 0.0 15 + -0.9x + 0.01x2 = 0.0 + -0.01x2 + 0.01x2 15 + -0.9x + 0.01x2 = -0.01x2 + 0.01x2 Combine like terms: -0.01x2 + 0.01x2 = 0.00 15 + -0.9x + 0.01x2 = 0.00 Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. 1500 + -90x + x2 = 0 Move the constant term to the right: Add '-1500' to each side of the equation. 1500 + -90x + -1500 + x2 = 0 + -1500 Reorder the terms: 1500 + -1500 + -90x + x2 = 0 + -1500 Combine like terms: 1500 + -1500 = 0 0 + -90x + x2 = 0 + -1500 -90x + x2 = 0 + -1500 Combine like terms: 0 + -1500 = -1500 -90x + x2 = -1500 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 = -1500 + 2025 Reorder the terms: 2025 + -90x + x2 = -1500 + 2025 Combine like terms: -1500 + 2025 = 525 2025 + -90x + x2 = 525 Factor a perfect square on the left side: (x + -45)(x + -45) = 525 Calculate the square root of the right side: 22.912878475 Break this problem into two subproblems by setting (x + -45) equal to 22.912878475 and -22.912878475.Subproblem 1
x + -45 = 22.912878475 Simplifying x + -45 = 22.912878475 Reorder the terms: -45 + x = 22.912878475 Solving -45 + x = 22.912878475 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 = 22.912878475 + 45 Combine like terms: -45 + 45 = 0 0 + x = 22.912878475 + 45 x = 22.912878475 + 45 Combine like terms: 22.912878475 + 45 = 67.912878475 x = 67.912878475 Simplifying x = 67.912878475Subproblem 2
x + -45 = -22.912878475 Simplifying x + -45 = -22.912878475 Reorder the terms: -45 + x = -22.912878475 Solving -45 + x = -22.912878475 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 = -22.912878475 + 45 Combine like terms: -45 + 45 = 0 0 + x = -22.912878475 + 45 x = -22.912878475 + 45 Combine like terms: -22.912878475 + 45 = 22.087121525 x = 22.087121525 Simplifying x = 22.087121525Solution
The solution to the problem is based on the solutions from the subproblems. x = {67.912878475, 22.087121525}
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