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Simplifying 25x2 + -82x + 63 = 0 Reorder the terms: 63 + -82x + 25x2 = 0 Solving 63 + -82x + 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'. 2.52 + -3.28x + x2 = 0 Move the constant term to the right: Add '-2.52' to each side of the equation. 2.52 + -3.28x + -2.52 + x2 = 0 + -2.52 Reorder the terms: 2.52 + -2.52 + -3.28x + x2 = 0 + -2.52 Combine like terms: 2.52 + -2.52 = 0.00 0.00 + -3.28x + x2 = 0 + -2.52 -3.28x + x2 = 0 + -2.52 Combine like terms: 0 + -2.52 = -2.52 -3.28x + x2 = -2.52 The x term is -3.28x. Take half its coefficient (-1.64). Square it (2.6896) and add it to both sides. Add '2.6896' to each side of the equation. -3.28x + 2.6896 + x2 = -2.52 + 2.6896 Reorder the terms: 2.6896 + -3.28x + x2 = -2.52 + 2.6896 Combine like terms: -2.52 + 2.6896 = 0.1696 2.6896 + -3.28x + x2 = 0.1696 Factor a perfect square on the left side: (x + -1.64)(x + -1.64) = 0.1696 Calculate the square root of the right side: 0.411825206 Break this problem into two subproblems by setting (x + -1.64) equal to 0.411825206 and -0.411825206.Subproblem 1
x + -1.64 = 0.411825206 Simplifying x + -1.64 = 0.411825206 Reorder the terms: -1.64 + x = 0.411825206 Solving -1.64 + x = 0.411825206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.64' to each side of the equation. -1.64 + 1.64 + x = 0.411825206 + 1.64 Combine like terms: -1.64 + 1.64 = 0.00 0.00 + x = 0.411825206 + 1.64 x = 0.411825206 + 1.64 Combine like terms: 0.411825206 + 1.64 = 2.051825206 x = 2.051825206 Simplifying x = 2.051825206Subproblem 2
x + -1.64 = -0.411825206 Simplifying x + -1.64 = -0.411825206 Reorder the terms: -1.64 + x = -0.411825206 Solving -1.64 + x = -0.411825206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.64' to each side of the equation. -1.64 + 1.64 + x = -0.411825206 + 1.64 Combine like terms: -1.64 + 1.64 = 0.00 0.00 + x = -0.411825206 + 1.64 x = -0.411825206 + 1.64 Combine like terms: -0.411825206 + 1.64 = 1.228174794 x = 1.228174794 Simplifying x = 1.228174794Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.051825206, 1.228174794}
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