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Simplifying 14x2 + 28x = 9 Reorder the terms: 28x + 14x2 = 9 Solving 28x + 14x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + 28x + 14x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 28x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.6428571429 + 2x + x2 = 0 Move the constant term to the right: Add '0.6428571429' to each side of the equation. -0.6428571429 + 2x + 0.6428571429 + x2 = 0 + 0.6428571429 Reorder the terms: -0.6428571429 + 0.6428571429 + 2x + x2 = 0 + 0.6428571429 Combine like terms: -0.6428571429 + 0.6428571429 = 0.0000000000 0.0000000000 + 2x + x2 = 0 + 0.6428571429 2x + x2 = 0 + 0.6428571429 Combine like terms: 0 + 0.6428571429 = 0.6428571429 2x + x2 = 0.6428571429 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 0.6428571429 + 1 Reorder the terms: 1 + 2x + x2 = 0.6428571429 + 1 Combine like terms: 0.6428571429 + 1 = 1.6428571429 1 + 2x + x2 = 1.6428571429 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.6428571429 Calculate the square root of the right side: 1.281739889 Break this problem into two subproblems by setting (x + 1) equal to 1.281739889 and -1.281739889.Subproblem 1
x + 1 = 1.281739889 Simplifying x + 1 = 1.281739889 Reorder the terms: 1 + x = 1.281739889 Solving 1 + x = 1.281739889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.281739889 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.281739889 + -1 x = 1.281739889 + -1 Combine like terms: 1.281739889 + -1 = 0.281739889 x = 0.281739889 Simplifying x = 0.281739889Subproblem 2
x + 1 = -1.281739889 Simplifying x + 1 = -1.281739889 Reorder the terms: 1 + x = -1.281739889 Solving 1 + x = -1.281739889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.281739889 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.281739889 + -1 x = -1.281739889 + -1 Combine like terms: -1.281739889 + -1 = -2.281739889 x = -2.281739889 Simplifying x = -2.281739889Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.281739889, -2.281739889}
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