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Simplifying 9x2 + -10x + -63 = 0 Reorder the terms: -63 + -10x + 9x2 = 0 Solving -63 + -10x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -7 + -1.111111111x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -1.111111111x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -1.111111111x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1.111111111x + x2 = 0 + 7 -1.111111111x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -1.111111111x + x2 = 7 The x term is -1.111111111x. Take half its coefficient (-0.5555555555). Square it (0.3086419752) and add it to both sides. Add '0.3086419752' to each side of the equation. -1.111111111x + 0.3086419752 + x2 = 7 + 0.3086419752 Reorder the terms: 0.3086419752 + -1.111111111x + x2 = 7 + 0.3086419752 Combine like terms: 7 + 0.3086419752 = 7.3086419752 0.3086419752 + -1.111111111x + x2 = 7.3086419752 Factor a perfect square on the left side: (x + -0.5555555555)(x + -0.5555555555) = 7.3086419752 Calculate the square root of the right side: 2.703450013 Break this problem into two subproblems by setting (x + -0.5555555555) equal to 2.703450013 and -2.703450013.Subproblem 1
x + -0.5555555555 = 2.703450013 Simplifying x + -0.5555555555 = 2.703450013 Reorder the terms: -0.5555555555 + x = 2.703450013 Solving -0.5555555555 + x = 2.703450013 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5555555555' to each side of the equation. -0.5555555555 + 0.5555555555 + x = 2.703450013 + 0.5555555555 Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000 0.0000000000 + x = 2.703450013 + 0.5555555555 x = 2.703450013 + 0.5555555555 Combine like terms: 2.703450013 + 0.5555555555 = 3.2590055685 x = 3.2590055685 Simplifying x = 3.2590055685Subproblem 2
x + -0.5555555555 = -2.703450013 Simplifying x + -0.5555555555 = -2.703450013 Reorder the terms: -0.5555555555 + x = -2.703450013 Solving -0.5555555555 + x = -2.703450013 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5555555555' to each side of the equation. -0.5555555555 + 0.5555555555 + x = -2.703450013 + 0.5555555555 Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000 0.0000000000 + x = -2.703450013 + 0.5555555555 x = -2.703450013 + 0.5555555555 Combine like terms: -2.703450013 + 0.5555555555 = -2.1478944575 x = -2.1478944575 Simplifying x = -2.1478944575Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.2590055685, -2.1478944575}
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