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Simplifying -13.156x2 + 254.447x + 5471.082 = 0 Reorder the terms: 5471.082 + 254.447x + -13.156x2 = 0 Solving 5471.082 + 254.447x + -13.156x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -13.156 the coefficient of the squared term: Divide each side by '-13.156'. -415.8621161 + -19.34075707x + x2 = 0 Move the constant term to the right: Add '415.8621161' to each side of the equation. -415.8621161 + -19.34075707x + 415.8621161 + x2 = 0 + 415.8621161 Reorder the terms: -415.8621161 + 415.8621161 + -19.34075707x + x2 = 0 + 415.8621161 Combine like terms: -415.8621161 + 415.8621161 = 0.0000000 0.0000000 + -19.34075707x + x2 = 0 + 415.8621161 -19.34075707x + x2 = 0 + 415.8621161 Combine like terms: 0 + 415.8621161 = 415.8621161 -19.34075707x + x2 = 415.8621161 The x term is -19.34075707x. Take half its coefficient (-9.670378535). Square it (93.51622101) and add it to both sides. Add '93.51622101' to each side of the equation. -19.34075707x + 93.51622101 + x2 = 415.8621161 + 93.51622101 Reorder the terms: 93.51622101 + -19.34075707x + x2 = 415.8621161 + 93.51622101 Combine like terms: 415.8621161 + 93.51622101 = 509.37833711 93.51622101 + -19.34075707x + x2 = 509.37833711 Factor a perfect square on the left side: (x + -9.670378535)(x + -9.670378535) = 509.37833711 Calculate the square root of the right side: 22.569411537 Break this problem into two subproblems by setting (x + -9.670378535) equal to 22.569411537 and -22.569411537.Subproblem 1
x + -9.670378535 = 22.569411537 Simplifying x + -9.670378535 = 22.569411537 Reorder the terms: -9.670378535 + x = 22.569411537 Solving -9.670378535 + x = 22.569411537 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.670378535' to each side of the equation. -9.670378535 + 9.670378535 + x = 22.569411537 + 9.670378535 Combine like terms: -9.670378535 + 9.670378535 = 0.000000000 0.000000000 + x = 22.569411537 + 9.670378535 x = 22.569411537 + 9.670378535 Combine like terms: 22.569411537 + 9.670378535 = 32.239790072 x = 32.239790072 Simplifying x = 32.239790072Subproblem 2
x + -9.670378535 = -22.569411537 Simplifying x + -9.670378535 = -22.569411537 Reorder the terms: -9.670378535 + x = -22.569411537 Solving -9.670378535 + x = -22.569411537 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.670378535' to each side of the equation. -9.670378535 + 9.670378535 + x = -22.569411537 + 9.670378535 Combine like terms: -9.670378535 + 9.670378535 = 0.000000000 0.000000000 + x = -22.569411537 + 9.670378535 x = -22.569411537 + 9.670378535 Combine like terms: -22.569411537 + 9.670378535 = -12.899033002 x = -12.899033002 Simplifying x = -12.899033002Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.239790072, -12.899033002}
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