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Simplifying -0.19x2 + 1.2x + 7.6 = 0 Reorder the terms: 7.6 + 1.2x + -0.19x2 = 0 Solving 7.6 + 1.2x + -0.19x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.19 the coefficient of the squared term: Divide each side by '-0.19'. -40 + -6.315789474x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + -6.315789474x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + -6.315789474x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -6.315789474x + x2 = 0 + 40 -6.315789474x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 -6.315789474x + x2 = 40 The x term is -6.315789474x. Take half its coefficient (-3.157894737). Square it (9.972299170) and add it to both sides. Add '9.972299170' to each side of the equation. -6.315789474x + 9.972299170 + x2 = 40 + 9.972299170 Reorder the terms: 9.972299170 + -6.315789474x + x2 = 40 + 9.972299170 Combine like terms: 40 + 9.972299170 = 49.97229917 9.972299170 + -6.315789474x + x2 = 49.97229917 Factor a perfect square on the left side: (x + -3.157894737)(x + -3.157894737) = 49.97229917 Calculate the square root of the right side: 7.069108796 Break this problem into two subproblems by setting (x + -3.157894737) equal to 7.069108796 and -7.069108796.Subproblem 1
x + -3.157894737 = 7.069108796 Simplifying x + -3.157894737 = 7.069108796 Reorder the terms: -3.157894737 + x = 7.069108796 Solving -3.157894737 + x = 7.069108796 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.157894737' to each side of the equation. -3.157894737 + 3.157894737 + x = 7.069108796 + 3.157894737 Combine like terms: -3.157894737 + 3.157894737 = 0.000000000 0.000000000 + x = 7.069108796 + 3.157894737 x = 7.069108796 + 3.157894737 Combine like terms: 7.069108796 + 3.157894737 = 10.227003533 x = 10.227003533 Simplifying x = 10.227003533Subproblem 2
x + -3.157894737 = -7.069108796 Simplifying x + -3.157894737 = -7.069108796 Reorder the terms: -3.157894737 + x = -7.069108796 Solving -3.157894737 + x = -7.069108796 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.157894737' to each side of the equation. -3.157894737 + 3.157894737 + x = -7.069108796 + 3.157894737 Combine like terms: -3.157894737 + 3.157894737 = 0.000000000 0.000000000 + x = -7.069108796 + 3.157894737 x = -7.069108796 + 3.157894737 Combine like terms: -7.069108796 + 3.157894737 = -3.911214059 x = -3.911214059 Simplifying x = -3.911214059Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.227003533, -3.911214059}
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