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Simplifying 19 * 13x2 + -12 * 13x + -100 = 0 Multiply 19 * 13 247x2 + -12 * 13x + -100 = 0 Multiply -12 * 13 247x2 + -156x + -100 = 0 Reorder the terms: -100 + -156x + 247x2 = 0 Solving -100 + -156x + 247x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 247 the coefficient of the squared term: Divide each side by '247'. -0.4048582996 + -0.6315789474x + x2 = 0 Move the constant term to the right: Add '0.4048582996' to each side of the equation. -0.4048582996 + -0.6315789474x + 0.4048582996 + x2 = 0 + 0.4048582996 Reorder the terms: -0.4048582996 + 0.4048582996 + -0.6315789474x + x2 = 0 + 0.4048582996 Combine like terms: -0.4048582996 + 0.4048582996 = 0.0000000000 0.0000000000 + -0.6315789474x + x2 = 0 + 0.4048582996 -0.6315789474x + x2 = 0 + 0.4048582996 Combine like terms: 0 + 0.4048582996 = 0.4048582996 -0.6315789474x + x2 = 0.4048582996 The x term is -0.6315789474x. Take half its coefficient (-0.3157894737). Square it (0.09972299170) and add it to both sides. Add '0.09972299170' to each side of the equation. -0.6315789474x + 0.09972299170 + x2 = 0.4048582996 + 0.09972299170 Reorder the terms: 0.09972299170 + -0.6315789474x + x2 = 0.4048582996 + 0.09972299170 Combine like terms: 0.4048582996 + 0.09972299170 = 0.5045812913 0.09972299170 + -0.6315789474x + x2 = 0.5045812913 Factor a perfect square on the left side: (x + -0.3157894737)(x + -0.3157894737) = 0.5045812913 Calculate the square root of the right side: 0.710338857 Break this problem into two subproblems by setting (x + -0.3157894737) equal to 0.710338857 and -0.710338857.Subproblem 1
x + -0.3157894737 = 0.710338857 Simplifying x + -0.3157894737 = 0.710338857 Reorder the terms: -0.3157894737 + x = 0.710338857 Solving -0.3157894737 + x = 0.710338857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3157894737' to each side of the equation. -0.3157894737 + 0.3157894737 + x = 0.710338857 + 0.3157894737 Combine like terms: -0.3157894737 + 0.3157894737 = 0.0000000000 0.0000000000 + x = 0.710338857 + 0.3157894737 x = 0.710338857 + 0.3157894737 Combine like terms: 0.710338857 + 0.3157894737 = 1.0261283307 x = 1.0261283307 Simplifying x = 1.0261283307Subproblem 2
x + -0.3157894737 = -0.710338857 Simplifying x + -0.3157894737 = -0.710338857 Reorder the terms: -0.3157894737 + x = -0.710338857 Solving -0.3157894737 + x = -0.710338857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3157894737' to each side of the equation. -0.3157894737 + 0.3157894737 + x = -0.710338857 + 0.3157894737 Combine like terms: -0.3157894737 + 0.3157894737 = 0.0000000000 0.0000000000 + x = -0.710338857 + 0.3157894737 x = -0.710338857 + 0.3157894737 Combine like terms: -0.710338857 + 0.3157894737 = -0.3945493833 x = -0.3945493833 Simplifying x = -0.3945493833Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0261283307, -0.3945493833}
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