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Simplifying 8x2 + -35x + 35 = 0 Reorder the terms: 35 + -35x + 8x2 = 0 Solving 35 + -35x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 4.375 + -4.375x + x2 = 0 Move the constant term to the right: Add '-4.375' to each side of the equation. 4.375 + -4.375x + -4.375 + x2 = 0 + -4.375 Reorder the terms: 4.375 + -4.375 + -4.375x + x2 = 0 + -4.375 Combine like terms: 4.375 + -4.375 = 0.000 0.000 + -4.375x + x2 = 0 + -4.375 -4.375x + x2 = 0 + -4.375 Combine like terms: 0 + -4.375 = -4.375 -4.375x + x2 = -4.375 The x term is -4.375x. Take half its coefficient (-2.1875). Square it (4.78515625) and add it to both sides. Add '4.78515625' to each side of the equation. -4.375x + 4.78515625 + x2 = -4.375 + 4.78515625 Reorder the terms: 4.78515625 + -4.375x + x2 = -4.375 + 4.78515625 Combine like terms: -4.375 + 4.78515625 = 0.41015625 4.78515625 + -4.375x + x2 = 0.41015625 Factor a perfect square on the left side: (x + -2.1875)(x + -2.1875) = 0.41015625 Calculate the square root of the right side: 0.640434423 Break this problem into two subproblems by setting (x + -2.1875) equal to 0.640434423 and -0.640434423.Subproblem 1
x + -2.1875 = 0.640434423 Simplifying x + -2.1875 = 0.640434423 Reorder the terms: -2.1875 + x = 0.640434423 Solving -2.1875 + x = 0.640434423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.1875' to each side of the equation. -2.1875 + 2.1875 + x = 0.640434423 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + x = 0.640434423 + 2.1875 x = 0.640434423 + 2.1875 Combine like terms: 0.640434423 + 2.1875 = 2.827934423 x = 2.827934423 Simplifying x = 2.827934423Subproblem 2
x + -2.1875 = -0.640434423 Simplifying x + -2.1875 = -0.640434423 Reorder the terms: -2.1875 + x = -0.640434423 Solving -2.1875 + x = -0.640434423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.1875' to each side of the equation. -2.1875 + 2.1875 + x = -0.640434423 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + x = -0.640434423 + 2.1875 x = -0.640434423 + 2.1875 Combine like terms: -0.640434423 + 2.1875 = 1.547065577 x = 1.547065577 Simplifying x = 1.547065577Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.827934423, 1.547065577}
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