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Simplifying 25x2 + -90x + 81 = 12 Reorder the terms: 81 + -90x + 25x2 = 12 Solving 81 + -90x + 25x2 = 12 Solving for variable 'x'. Reorder the terms: 81 + -12 + -90x + 25x2 = 12 + -12 Combine like terms: 81 + -12 = 69 69 + -90x + 25x2 = 12 + -12 Combine like terms: 12 + -12 = 0 69 + -90x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 2.76 + -3.6x + x2 = 0 Move the constant term to the right: Add '-2.76' to each side of the equation. 2.76 + -3.6x + -2.76 + x2 = 0 + -2.76 Reorder the terms: 2.76 + -2.76 + -3.6x + x2 = 0 + -2.76 Combine like terms: 2.76 + -2.76 = 0.00 0.00 + -3.6x + x2 = 0 + -2.76 -3.6x + x2 = 0 + -2.76 Combine like terms: 0 + -2.76 = -2.76 -3.6x + x2 = -2.76 The x term is -3.6x. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6x + 3.24 + x2 = -2.76 + 3.24 Reorder the terms: 3.24 + -3.6x + x2 = -2.76 + 3.24 Combine like terms: -2.76 + 3.24 = 0.48 3.24 + -3.6x + x2 = 0.48 Factor a perfect square on the left side: (x + -1.8)(x + -1.8) = 0.48 Calculate the square root of the right side: 0.692820323 Break this problem into two subproblems by setting (x + -1.8) equal to 0.692820323 and -0.692820323.Subproblem 1
x + -1.8 = 0.692820323 Simplifying x + -1.8 = 0.692820323 Reorder the terms: -1.8 + x = 0.692820323 Solving -1.8 + x = 0.692820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = 0.692820323 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 0.692820323 + 1.8 x = 0.692820323 + 1.8 Combine like terms: 0.692820323 + 1.8 = 2.492820323 x = 2.492820323 Simplifying x = 2.492820323Subproblem 2
x + -1.8 = -0.692820323 Simplifying x + -1.8 = -0.692820323 Reorder the terms: -1.8 + x = -0.692820323 Solving -1.8 + x = -0.692820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = -0.692820323 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -0.692820323 + 1.8 x = -0.692820323 + 1.8 Combine like terms: -0.692820323 + 1.8 = 1.107179677 x = 1.107179677 Simplifying x = 1.107179677Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.492820323, 1.107179677}
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