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Simplifying -81 + 25x2 + -90x = 0 Reorder the terms: -81 + -90x + 25x2 = 0 Solving -81 + -90x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -3.24 + -3.6x + x2 = 0 Move the constant term to the right: Add '3.24' to each side of the equation. -3.24 + -3.6x + 3.24 + x2 = 0 + 3.24 Reorder the terms: -3.24 + 3.24 + -3.6x + x2 = 0 + 3.24 Combine like terms: -3.24 + 3.24 = 0.00 0.00 + -3.6x + x2 = 0 + 3.24 -3.6x + x2 = 0 + 3.24 Combine like terms: 0 + 3.24 = 3.24 -3.6x + x2 = 3.24 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 = 3.24 + 3.24 Reorder the terms: 3.24 + -3.6x + x2 = 3.24 + 3.24 Combine like terms: 3.24 + 3.24 = 6.48 3.24 + -3.6x + x2 = 6.48 Factor a perfect square on the left side: (x + -1.8)(x + -1.8) = 6.48 Calculate the square root of the right side: 2.545584412 Break this problem into two subproblems by setting (x + -1.8) equal to 2.545584412 and -2.545584412.Subproblem 1
x + -1.8 = 2.545584412 Simplifying x + -1.8 = 2.545584412 Reorder the terms: -1.8 + x = 2.545584412 Solving -1.8 + x = 2.545584412 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 = 2.545584412 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 2.545584412 + 1.8 x = 2.545584412 + 1.8 Combine like terms: 2.545584412 + 1.8 = 4.345584412 x = 4.345584412 Simplifying x = 4.345584412Subproblem 2
x + -1.8 = -2.545584412 Simplifying x + -1.8 = -2.545584412 Reorder the terms: -1.8 + x = -2.545584412 Solving -1.8 + x = -2.545584412 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 = -2.545584412 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -2.545584412 + 1.8 x = -2.545584412 + 1.8 Combine like terms: -2.545584412 + 1.8 = -0.745584412 x = -0.745584412 Simplifying x = -0.745584412Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.345584412, -0.745584412}
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