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Simplifying 0 = -9x2 + 13x + 1 Reorder the terms: 0 = 1 + 13x + -9x2 Solving 0 = 1 + 13x + -9x2 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + -13x + 9x2 = 1 + 13x + -9x2 + -1 + -13x + 9x2 Reorder the terms: -1 + -13x + 9x2 = 1 + -1 + 13x + -13x + -9x2 + 9x2 Combine like terms: 1 + -1 = 0 -1 + -13x + 9x2 = 0 + 13x + -13x + -9x2 + 9x2 -1 + -13x + 9x2 = 13x + -13x + -9x2 + 9x2 Combine like terms: 13x + -13x = 0 -1 + -13x + 9x2 = 0 + -9x2 + 9x2 -1 + -13x + 9x2 = -9x2 + 9x2 Combine like terms: -9x2 + 9x2 = 0 -1 + -13x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.1111111111 + -1.444444444x + x2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + -1.444444444x + 0.1111111111 + x2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + -1.444444444x + x2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + -1.444444444x + x2 = 0 + 0.1111111111 -1.444444444x + x2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 -1.444444444x + x2 = 0.1111111111 The x term is -1.444444444x. Take half its coefficient (-0.722222222). Square it (0.5216049380) and add it to both sides. Add '0.5216049380' to each side of the equation. -1.444444444x + 0.5216049380 + x2 = 0.1111111111 + 0.5216049380 Reorder the terms: 0.5216049380 + -1.444444444x + x2 = 0.1111111111 + 0.5216049380 Combine like terms: 0.1111111111 + 0.5216049380 = 0.6327160491 0.5216049380 + -1.444444444x + x2 = 0.6327160491 Factor a perfect square on the left side: (x + -0.722222222)(x + -0.722222222) = 0.6327160491 Calculate the square root of the right side: 0.795434503 Break this problem into two subproblems by setting (x + -0.722222222) equal to 0.795434503 and -0.795434503.Subproblem 1
x + -0.722222222 = 0.795434503 Simplifying x + -0.722222222 = 0.795434503 Reorder the terms: -0.722222222 + x = 0.795434503 Solving -0.722222222 + x = 0.795434503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.722222222' to each side of the equation. -0.722222222 + 0.722222222 + x = 0.795434503 + 0.722222222 Combine like terms: -0.722222222 + 0.722222222 = 0.000000000 0.000000000 + x = 0.795434503 + 0.722222222 x = 0.795434503 + 0.722222222 Combine like terms: 0.795434503 + 0.722222222 = 1.517656725 x = 1.517656725 Simplifying x = 1.517656725Subproblem 2
x + -0.722222222 = -0.795434503 Simplifying x + -0.722222222 = -0.795434503 Reorder the terms: -0.722222222 + x = -0.795434503 Solving -0.722222222 + x = -0.795434503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.722222222' to each side of the equation. -0.722222222 + 0.722222222 + x = -0.795434503 + 0.722222222 Combine like terms: -0.722222222 + 0.722222222 = 0.000000000 0.000000000 + x = -0.795434503 + 0.722222222 x = -0.795434503 + 0.722222222 Combine like terms: -0.795434503 + 0.722222222 = -0.073212281 x = -0.073212281 Simplifying x = -0.073212281Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.517656725, -0.073212281}
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