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Simplifying 9x2 + 4x2 + -18x + -13 = 0 Reorder the terms: -13 + -18x + 9x2 + 4x2 = 0 Combine like terms: 9x2 + 4x2 = 13x2 -13 + -18x + 13x2 = 0 Solving -13 + -18x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -1 + -1.384615385x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.384615385x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -1.384615385x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.384615385x + x2 = 0 + 1 -1.384615385x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.384615385x + x2 = 1 The x term is -1.384615385x. Take half its coefficient (-0.6923076925). Square it (0.4792899411) and add it to both sides. Add '0.4792899411' to each side of the equation. -1.384615385x + 0.4792899411 + x2 = 1 + 0.4792899411 Reorder the terms: 0.4792899411 + -1.384615385x + x2 = 1 + 0.4792899411 Combine like terms: 1 + 0.4792899411 = 1.4792899411 0.4792899411 + -1.384615385x + x2 = 1.4792899411 Factor a perfect square on the left side: (x + -0.6923076925)(x + -0.6923076925) = 1.4792899411 Calculate the square root of the right side: 1.216260639 Break this problem into two subproblems by setting (x + -0.6923076925) equal to 1.216260639 and -1.216260639.Subproblem 1
x + -0.6923076925 = 1.216260639 Simplifying x + -0.6923076925 = 1.216260639 Reorder the terms: -0.6923076925 + x = 1.216260639 Solving -0.6923076925 + x = 1.216260639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6923076925' to each side of the equation. -0.6923076925 + 0.6923076925 + x = 1.216260639 + 0.6923076925 Combine like terms: -0.6923076925 + 0.6923076925 = 0.0000000000 0.0000000000 + x = 1.216260639 + 0.6923076925 x = 1.216260639 + 0.6923076925 Combine like terms: 1.216260639 + 0.6923076925 = 1.9085683315 x = 1.9085683315 Simplifying x = 1.9085683315Subproblem 2
x + -0.6923076925 = -1.216260639 Simplifying x + -0.6923076925 = -1.216260639 Reorder the terms: -0.6923076925 + x = -1.216260639 Solving -0.6923076925 + x = -1.216260639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6923076925' to each side of the equation. -0.6923076925 + 0.6923076925 + x = -1.216260639 + 0.6923076925 Combine like terms: -0.6923076925 + 0.6923076925 = 0.0000000000 0.0000000000 + x = -1.216260639 + 0.6923076925 x = -1.216260639 + 0.6923076925 Combine like terms: -1.216260639 + 0.6923076925 = -0.5239529465 x = -0.5239529465 Simplifying x = -0.5239529465Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9085683315, -0.5239529465}
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