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Simplifying 14x2 + -24x + 3 = 0 Reorder the terms: 3 + -24x + 14x2 = 0 Solving 3 + -24x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 0.2142857143 + -1.714285714x + x2 = 0 Move the constant term to the right: Add '-0.2142857143' to each side of the equation. 0.2142857143 + -1.714285714x + -0.2142857143 + x2 = 0 + -0.2142857143 Reorder the terms: 0.2142857143 + -0.2142857143 + -1.714285714x + x2 = 0 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + -1.714285714x + x2 = 0 + -0.2142857143 -1.714285714x + x2 = 0 + -0.2142857143 Combine like terms: 0 + -0.2142857143 = -0.2142857143 -1.714285714x + x2 = -0.2142857143 The x term is -1.714285714x. Take half its coefficient (-0.857142857). Square it (0.7346938773) and add it to both sides. Add '0.7346938773' to each side of the equation. -1.714285714x + 0.7346938773 + x2 = -0.2142857143 + 0.7346938773 Reorder the terms: 0.7346938773 + -1.714285714x + x2 = -0.2142857143 + 0.7346938773 Combine like terms: -0.2142857143 + 0.7346938773 = 0.520408163 0.7346938773 + -1.714285714x + x2 = 0.520408163 Factor a perfect square on the left side: (x + -0.857142857)(x + -0.857142857) = 0.520408163 Calculate the square root of the right side: 0.72139321 Break this problem into two subproblems by setting (x + -0.857142857) equal to 0.72139321 and -0.72139321.Subproblem 1
x + -0.857142857 = 0.72139321 Simplifying x + -0.857142857 = 0.72139321 Reorder the terms: -0.857142857 + x = 0.72139321 Solving -0.857142857 + x = 0.72139321 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + x = 0.72139321 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + x = 0.72139321 + 0.857142857 x = 0.72139321 + 0.857142857 Combine like terms: 0.72139321 + 0.857142857 = 1.578536067 x = 1.578536067 Simplifying x = 1.578536067Subproblem 2
x + -0.857142857 = -0.72139321 Simplifying x + -0.857142857 = -0.72139321 Reorder the terms: -0.857142857 + x = -0.72139321 Solving -0.857142857 + x = -0.72139321 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + x = -0.72139321 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + x = -0.72139321 + 0.857142857 x = -0.72139321 + 0.857142857 Combine like terms: -0.72139321 + 0.857142857 = 0.135749647 x = 0.135749647 Simplifying x = 0.135749647Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.578536067, 0.135749647}
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