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Simplifying 18x + 13x2 = 4 Solving 18x + 13x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + 18x + 13x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 18x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -0.3076923077 + 1.384615385x + x2 = 0 Move the constant term to the right: Add '0.3076923077' to each side of the equation. -0.3076923077 + 1.384615385x + 0.3076923077 + x2 = 0 + 0.3076923077 Reorder the terms: -0.3076923077 + 0.3076923077 + 1.384615385x + x2 = 0 + 0.3076923077 Combine like terms: -0.3076923077 + 0.3076923077 = 0.0000000000 0.0000000000 + 1.384615385x + x2 = 0 + 0.3076923077 1.384615385x + x2 = 0 + 0.3076923077 Combine like terms: 0 + 0.3076923077 = 0.3076923077 1.384615385x + x2 = 0.3076923077 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 = 0.3076923077 + 0.4792899411 Reorder the terms: 0.4792899411 + 1.384615385x + x2 = 0.3076923077 + 0.4792899411 Combine like terms: 0.3076923077 + 0.4792899411 = 0.7869822488 0.4792899411 + 1.384615385x + x2 = 0.7869822488 Factor a perfect square on the left side: (x + 0.6923076925)(x + 0.6923076925) = 0.7869822488 Calculate the square root of the right side: 0.8871202 Break this problem into two subproblems by setting (x + 0.6923076925) equal to 0.8871202 and -0.8871202.Subproblem 1
x + 0.6923076925 = 0.8871202 Simplifying x + 0.6923076925 = 0.8871202 Reorder the terms: 0.6923076925 + x = 0.8871202 Solving 0.6923076925 + x = 0.8871202 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 = 0.8871202 + -0.6923076925 Combine like terms: 0.6923076925 + -0.6923076925 = 0.0000000000 0.0000000000 + x = 0.8871202 + -0.6923076925 x = 0.8871202 + -0.6923076925 Combine like terms: 0.8871202 + -0.6923076925 = 0.1948125075 x = 0.1948125075 Simplifying x = 0.1948125075Subproblem 2
x + 0.6923076925 = -0.8871202 Simplifying x + 0.6923076925 = -0.8871202 Reorder the terms: 0.6923076925 + x = -0.8871202 Solving 0.6923076925 + x = -0.8871202 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 = -0.8871202 + -0.6923076925 Combine like terms: 0.6923076925 + -0.6923076925 = 0.0000000000 0.0000000000 + x = -0.8871202 + -0.6923076925 x = -0.8871202 + -0.6923076925 Combine like terms: -0.8871202 + -0.6923076925 = -1.5794278925 x = -1.5794278925 Simplifying x = -1.5794278925Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1948125075, -1.5794278925}
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