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Simplifying -9x2 + 8x + -3 = -200 Reorder the terms: -3 + 8x + -9x2 = -200 Solving -3 + 8x + -9x2 = -200 Solving for variable 'x'. Reorder the terms: -3 + 200 + 8x + -9x2 = -200 + 200 Combine like terms: -3 + 200 = 197 197 + 8x + -9x2 = -200 + 200 Combine like terms: -200 + 200 = 0 197 + 8x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -21.88888889 + -0.8888888889x + x2 = 0 Move the constant term to the right: Add '21.88888889' to each side of the equation. -21.88888889 + -0.8888888889x + 21.88888889 + x2 = 0 + 21.88888889 Reorder the terms: -21.88888889 + 21.88888889 + -0.8888888889x + x2 = 0 + 21.88888889 Combine like terms: -21.88888889 + 21.88888889 = 0.00000000 0.00000000 + -0.8888888889x + x2 = 0 + 21.88888889 -0.8888888889x + x2 = 0 + 21.88888889 Combine like terms: 0 + 21.88888889 = 21.88888889 -0.8888888889x + x2 = 21.88888889 The x term is -0.8888888889x. Take half its coefficient (-0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. -0.8888888889x + 0.1975308642 + x2 = 21.88888889 + 0.1975308642 Reorder the terms: 0.1975308642 + -0.8888888889x + x2 = 21.88888889 + 0.1975308642 Combine like terms: 21.88888889 + 0.1975308642 = 22.0864197542 0.1975308642 + -0.8888888889x + x2 = 22.0864197542 Factor a perfect square on the left side: (x + -0.4444444445)(x + -0.4444444445) = 22.0864197542 Calculate the square root of the right side: 4.699619107 Break this problem into two subproblems by setting (x + -0.4444444445) equal to 4.699619107 and -4.699619107.Subproblem 1
x + -0.4444444445 = 4.699619107 Simplifying x + -0.4444444445 = 4.699619107 Reorder the terms: -0.4444444445 + x = 4.699619107 Solving -0.4444444445 + x = 4.699619107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + x = 4.699619107 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = 4.699619107 + 0.4444444445 x = 4.699619107 + 0.4444444445 Combine like terms: 4.699619107 + 0.4444444445 = 5.1440635515 x = 5.1440635515 Simplifying x = 5.1440635515Subproblem 2
x + -0.4444444445 = -4.699619107 Simplifying x + -0.4444444445 = -4.699619107 Reorder the terms: -0.4444444445 + x = -4.699619107 Solving -0.4444444445 + x = -4.699619107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + x = -4.699619107 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = -4.699619107 + 0.4444444445 x = -4.699619107 + 0.4444444445 Combine like terms: -4.699619107 + 0.4444444445 = -4.2551746625 x = -4.2551746625 Simplifying x = -4.2551746625Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.1440635515, -4.2551746625}
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