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Simplifying x2 + (9x)(9 + -1x) = 45 Remove parenthesis around (9x) x2 + 9x(9 + -1x) = 45 x2 + (9 * 9x + -1x * 9x) = 45 x2 + (81x + -9x2) = 45 Reorder the terms: 81x + x2 + -9x2 = 45 Combine like terms: x2 + -9x2 = -8x2 81x + -8x2 = 45 Solving 81x + -8x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + 81x + -8x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + 81x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 5.625 + -10.125x + x2 = 0 Move the constant term to the right: Add '-5.625' to each side of the equation. 5.625 + -10.125x + -5.625 + x2 = 0 + -5.625 Reorder the terms: 5.625 + -5.625 + -10.125x + x2 = 0 + -5.625 Combine like terms: 5.625 + -5.625 = 0.000 0.000 + -10.125x + x2 = 0 + -5.625 -10.125x + x2 = 0 + -5.625 Combine like terms: 0 + -5.625 = -5.625 -10.125x + x2 = -5.625 The x term is -10.125x. Take half its coefficient (-5.0625). Square it (25.62890625) and add it to both sides. Add '25.62890625' to each side of the equation. -10.125x + 25.62890625 + x2 = -5.625 + 25.62890625 Reorder the terms: 25.62890625 + -10.125x + x2 = -5.625 + 25.62890625 Combine like terms: -5.625 + 25.62890625 = 20.00390625 25.62890625 + -10.125x + x2 = 20.00390625 Factor a perfect square on the left side: (x + -5.0625)(x + -5.0625) = 20.00390625 Calculate the square root of the right side: 4.472572666 Break this problem into two subproblems by setting (x + -5.0625) equal to 4.472572666 and -4.472572666.Subproblem 1
x + -5.0625 = 4.472572666 Simplifying x + -5.0625 = 4.472572666 Reorder the terms: -5.0625 + x = 4.472572666 Solving -5.0625 + x = 4.472572666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.0625' to each side of the equation. -5.0625 + 5.0625 + x = 4.472572666 + 5.0625 Combine like terms: -5.0625 + 5.0625 = 0.0000 0.0000 + x = 4.472572666 + 5.0625 x = 4.472572666 + 5.0625 Combine like terms: 4.472572666 + 5.0625 = 9.535072666 x = 9.535072666 Simplifying x = 9.535072666Subproblem 2
x + -5.0625 = -4.472572666 Simplifying x + -5.0625 = -4.472572666 Reorder the terms: -5.0625 + x = -4.472572666 Solving -5.0625 + x = -4.472572666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.0625' to each side of the equation. -5.0625 + 5.0625 + x = -4.472572666 + 5.0625 Combine like terms: -5.0625 + 5.0625 = 0.0000 0.0000 + x = -4.472572666 + 5.0625 x = -4.472572666 + 5.0625 Combine like terms: -4.472572666 + 5.0625 = 0.589927334 x = 0.589927334 Simplifying x = 0.589927334Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.535072666, 0.589927334}
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