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Simplifying 8x2 + 1 = 14x Reorder the terms: 1 + 8x2 = 14x Solving 1 + 8x2 = 14x Solving for variable 'x'. Reorder the terms: 1 + -14x + 8x2 = 14x + -14x Combine like terms: 14x + -14x = 0 1 + -14x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.125 + -1.75x + x2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + -1.75x + -0.125 + x2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + -1.75x + x2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + -1.75x + x2 = 0 + -0.125 -1.75x + x2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 -1.75x + x2 = -0.125 The x term is -1.75x. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75x + 0.765625 + x2 = -0.125 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = -0.125 + 0.765625 Combine like terms: -0.125 + 0.765625 = 0.640625 0.765625 + -1.75x + x2 = 0.640625 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = 0.640625 Calculate the square root of the right side: 0.80039053 Break this problem into two subproblems by setting (x + -0.875) equal to 0.80039053 and -0.80039053.Subproblem 1
x + -0.875 = 0.80039053 Simplifying x + -0.875 = 0.80039053 Reorder the terms: -0.875 + x = 0.80039053 Solving -0.875 + x = 0.80039053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = 0.80039053 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 0.80039053 + 0.875 x = 0.80039053 + 0.875 Combine like terms: 0.80039053 + 0.875 = 1.67539053 x = 1.67539053 Simplifying x = 1.67539053Subproblem 2
x + -0.875 = -0.80039053 Simplifying x + -0.875 = -0.80039053 Reorder the terms: -0.875 + x = -0.80039053 Solving -0.875 + x = -0.80039053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = -0.80039053 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -0.80039053 + 0.875 x = -0.80039053 + 0.875 Combine like terms: -0.80039053 + 0.875 = 0.07460947 x = 0.07460947 Simplifying x = 0.07460947Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.67539053, 0.07460947}
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