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Simplifying 8x2 + -73x + 70 = 0 Reorder the terms: 70 + -73x + 8x2 = 0 Solving 70 + -73x + 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'. 8.75 + -9.125x + x2 = 0 Move the constant term to the right: Add '-8.75' to each side of the equation. 8.75 + -9.125x + -8.75 + x2 = 0 + -8.75 Reorder the terms: 8.75 + -8.75 + -9.125x + x2 = 0 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + -9.125x + x2 = 0 + -8.75 -9.125x + x2 = 0 + -8.75 Combine like terms: 0 + -8.75 = -8.75 -9.125x + x2 = -8.75 The x term is -9.125x. Take half its coefficient (-4.5625). Square it (20.81640625) and add it to both sides. Add '20.81640625' to each side of the equation. -9.125x + 20.81640625 + x2 = -8.75 + 20.81640625 Reorder the terms: 20.81640625 + -9.125x + x2 = -8.75 + 20.81640625 Combine like terms: -8.75 + 20.81640625 = 12.06640625 20.81640625 + -9.125x + x2 = 12.06640625 Factor a perfect square on the left side: (x + -4.5625)(x + -4.5625) = 12.06640625 Calculate the square root of the right side: 3.473673308 Break this problem into two subproblems by setting (x + -4.5625) equal to 3.473673308 and -3.473673308.Subproblem 1
x + -4.5625 = 3.473673308 Simplifying x + -4.5625 = 3.473673308 Reorder the terms: -4.5625 + x = 3.473673308 Solving -4.5625 + x = 3.473673308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5625' to each side of the equation. -4.5625 + 4.5625 + x = 3.473673308 + 4.5625 Combine like terms: -4.5625 + 4.5625 = 0.0000 0.0000 + x = 3.473673308 + 4.5625 x = 3.473673308 + 4.5625 Combine like terms: 3.473673308 + 4.5625 = 8.036173308 x = 8.036173308 Simplifying x = 8.036173308Subproblem 2
x + -4.5625 = -3.473673308 Simplifying x + -4.5625 = -3.473673308 Reorder the terms: -4.5625 + x = -3.473673308 Solving -4.5625 + x = -3.473673308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5625' to each side of the equation. -4.5625 + 4.5625 + x = -3.473673308 + 4.5625 Combine like terms: -4.5625 + 4.5625 = 0.0000 0.0000 + x = -3.473673308 + 4.5625 x = -3.473673308 + 4.5625 Combine like terms: -3.473673308 + 4.5625 = 1.088826692 x = 1.088826692 Simplifying x = 1.088826692Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.036173308, 1.088826692}
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