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Simplifying 7x2 + -14x = 3 Reorder the terms: -14x + 7x2 = 3 Solving -14x + 7x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + -14x + 7x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -14x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.4285714286 + -2x + x2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + -2x + 0.4285714286 + x2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + -2x + x2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + -2x + x2 = 0 + 0.4285714286 -2x + x2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 -2x + x2 = 0.4285714286 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 = 0.4285714286 + 1 Reorder the terms: 1 + -2x + x2 = 0.4285714286 + 1 Combine like terms: 0.4285714286 + 1 = 1.4285714286 1 + -2x + x2 = 1.4285714286 Factor a perfect square on the left side: (x + -1)(x + -1) = 1.4285714286 Calculate the square root of the right side: 1.195228609 Break this problem into two subproblems by setting (x + -1) equal to 1.195228609 and -1.195228609.Subproblem 1
x + -1 = 1.195228609 Simplifying x + -1 = 1.195228609 Reorder the terms: -1 + x = 1.195228609 Solving -1 + x = 1.195228609 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 = 1.195228609 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.195228609 + 1 x = 1.195228609 + 1 Combine like terms: 1.195228609 + 1 = 2.195228609 x = 2.195228609 Simplifying x = 2.195228609Subproblem 2
x + -1 = -1.195228609 Simplifying x + -1 = -1.195228609 Reorder the terms: -1 + x = -1.195228609 Solving -1 + x = -1.195228609 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 = -1.195228609 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.195228609 + 1 x = -1.195228609 + 1 Combine like terms: -1.195228609 + 1 = -0.195228609 x = -0.195228609 Simplifying x = -0.195228609Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.195228609, -0.195228609}
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