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Simplifying 25x2 + -20x + 9 = 81 Reorder the terms: 9 + -20x + 25x2 = 81 Solving 9 + -20x + 25x2 = 81 Solving for variable 'x'. Reorder the terms: 9 + -81 + -20x + 25x2 = 81 + -81 Combine like terms: 9 + -81 = -72 -72 + -20x + 25x2 = 81 + -81 Combine like terms: 81 + -81 = 0 -72 + -20x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -2.88 + -0.8x + x2 = 0 Move the constant term to the right: Add '2.88' to each side of the equation. -2.88 + -0.8x + 2.88 + x2 = 0 + 2.88 Reorder the terms: -2.88 + 2.88 + -0.8x + x2 = 0 + 2.88 Combine like terms: -2.88 + 2.88 = 0.00 0.00 + -0.8x + x2 = 0 + 2.88 -0.8x + x2 = 0 + 2.88 Combine like terms: 0 + 2.88 = 2.88 -0.8x + x2 = 2.88 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 2.88 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 2.88 + 0.16 Combine like terms: 2.88 + 0.16 = 3.04 0.16 + -0.8x + x2 = 3.04 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 3.04 Calculate the square root of the right side: 1.743559577 Break this problem into two subproblems by setting (x + -0.4) equal to 1.743559577 and -1.743559577.Subproblem 1
x + -0.4 = 1.743559577 Simplifying x + -0.4 = 1.743559577 Reorder the terms: -0.4 + x = 1.743559577 Solving -0.4 + x = 1.743559577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 1.743559577 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 1.743559577 + 0.4 x = 1.743559577 + 0.4 Combine like terms: 1.743559577 + 0.4 = 2.143559577 x = 2.143559577 Simplifying x = 2.143559577Subproblem 2
x + -0.4 = -1.743559577 Simplifying x + -0.4 = -1.743559577 Reorder the terms: -0.4 + x = -1.743559577 Solving -0.4 + x = -1.743559577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -1.743559577 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -1.743559577 + 0.4 x = -1.743559577 + 0.4 Combine like terms: -1.743559577 + 0.4 = -1.343559577 x = -1.343559577 Simplifying x = -1.343559577Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.143559577, -1.343559577}
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