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Simplifying 14x * x + 7x + -170 = 0 Multiply x * x 14x2 + 7x + -170 = 0 Reorder the terms: -170 + 7x + 14x2 = 0 Solving -170 + 7x + 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'. -12.14285714 + 0.5x + x2 = 0 Move the constant term to the right: Add '12.14285714' to each side of the equation. -12.14285714 + 0.5x + 12.14285714 + x2 = 0 + 12.14285714 Reorder the terms: -12.14285714 + 12.14285714 + 0.5x + x2 = 0 + 12.14285714 Combine like terms: -12.14285714 + 12.14285714 = 0.00000000 0.00000000 + 0.5x + x2 = 0 + 12.14285714 0.5x + x2 = 0 + 12.14285714 Combine like terms: 0 + 12.14285714 = 12.14285714 0.5x + x2 = 12.14285714 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 12.14285714 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 12.14285714 + 0.0625 Combine like terms: 12.14285714 + 0.0625 = 12.20535714 0.0625 + 0.5x + x2 = 12.20535714 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 12.20535714 Calculate the square root of the right side: 3.493616628 Break this problem into two subproblems by setting (x + 0.25) equal to 3.493616628 and -3.493616628.Subproblem 1
x + 0.25 = 3.493616628 Simplifying x + 0.25 = 3.493616628 Reorder the terms: 0.25 + x = 3.493616628 Solving 0.25 + x = 3.493616628 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 3.493616628 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 3.493616628 + -0.25 x = 3.493616628 + -0.25 Combine like terms: 3.493616628 + -0.25 = 3.243616628 x = 3.243616628 Simplifying x = 3.243616628Subproblem 2
x + 0.25 = -3.493616628 Simplifying x + 0.25 = -3.493616628 Reorder the terms: 0.25 + x = -3.493616628 Solving 0.25 + x = -3.493616628 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -3.493616628 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -3.493616628 + -0.25 x = -3.493616628 + -0.25 Combine like terms: -3.493616628 + -0.25 = -3.743616628 x = -3.743616628 Simplifying x = -3.743616628Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.243616628, -3.743616628}
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