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Simplifying 0 = 7x2 + -26x + -14 Reorder the terms: 0 = -14 + -26x + 7x2 Solving 0 = -14 + -26x + 7x2 Solving for variable 'x'. Combine like terms: 0 + 14 = 14 14 + 26x + -7x2 = -14 + -26x + 7x2 + 14 + 26x + -7x2 Reorder the terms: 14 + 26x + -7x2 = -14 + 14 + -26x + 26x + 7x2 + -7x2 Combine like terms: -14 + 14 = 0 14 + 26x + -7x2 = 0 + -26x + 26x + 7x2 + -7x2 14 + 26x + -7x2 = -26x + 26x + 7x2 + -7x2 Combine like terms: -26x + 26x = 0 14 + 26x + -7x2 = 0 + 7x2 + -7x2 14 + 26x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 14 + 26x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -2 + -3.714285714x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -3.714285714x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -3.714285714x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3.714285714x + x2 = 0 + 2 -3.714285714x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -3.714285714x + x2 = 2 The x term is -3.714285714x. Take half its coefficient (-1.857142857). Square it (3.448979591) and add it to both sides. Add '3.448979591' to each side of the equation. -3.714285714x + 3.448979591 + x2 = 2 + 3.448979591 Reorder the terms: 3.448979591 + -3.714285714x + x2 = 2 + 3.448979591 Combine like terms: 2 + 3.448979591 = 5.448979591 3.448979591 + -3.714285714x + x2 = 5.448979591 Factor a perfect square on the left side: (x + -1.857142857)(x + -1.857142857) = 5.448979591 Calculate the square root of the right side: 2.334304948 Break this problem into two subproblems by setting (x + -1.857142857) equal to 2.334304948 and -2.334304948.Subproblem 1
x + -1.857142857 = 2.334304948 Simplifying x + -1.857142857 = 2.334304948 Reorder the terms: -1.857142857 + x = 2.334304948 Solving -1.857142857 + x = 2.334304948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.857142857' to each side of the equation. -1.857142857 + 1.857142857 + x = 2.334304948 + 1.857142857 Combine like terms: -1.857142857 + 1.857142857 = 0.000000000 0.000000000 + x = 2.334304948 + 1.857142857 x = 2.334304948 + 1.857142857 Combine like terms: 2.334304948 + 1.857142857 = 4.191447805 x = 4.191447805 Simplifying x = 4.191447805Subproblem 2
x + -1.857142857 = -2.334304948 Simplifying x + -1.857142857 = -2.334304948 Reorder the terms: -1.857142857 + x = -2.334304948 Solving -1.857142857 + x = -2.334304948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.857142857' to each side of the equation. -1.857142857 + 1.857142857 + x = -2.334304948 + 1.857142857 Combine like terms: -1.857142857 + 1.857142857 = 0.000000000 0.000000000 + x = -2.334304948 + 1.857142857 x = -2.334304948 + 1.857142857 Combine like terms: -2.334304948 + 1.857142857 = -0.477162091 x = -0.477162091 Simplifying x = -0.477162091Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.191447805, -0.477162091}
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