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Simplifying 8x2 + 27x + -70 = 0 Reorder the terms: -70 + 27x + 8x2 = 0 Solving -70 + 27x + 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 + 3.375x + x2 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + 3.375x + 8.75 + x2 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + 3.375x + x2 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + 3.375x + x2 = 0 + 8.75 3.375x + x2 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 3.375x + x2 = 8.75 The x term is 3.375x. Take half its coefficient (1.6875). Square it (2.84765625) and add it to both sides. Add '2.84765625' to each side of the equation. 3.375x + 2.84765625 + x2 = 8.75 + 2.84765625 Reorder the terms: 2.84765625 + 3.375x + x2 = 8.75 + 2.84765625 Combine like terms: 8.75 + 2.84765625 = 11.59765625 2.84765625 + 3.375x + x2 = 11.59765625 Factor a perfect square on the left side: (x + 1.6875)(x + 1.6875) = 11.59765625 Calculate the square root of the right side: 3.405533181 Break this problem into two subproblems by setting (x + 1.6875) equal to 3.405533181 and -3.405533181.Subproblem 1
x + 1.6875 = 3.405533181 Simplifying x + 1.6875 = 3.405533181 Reorder the terms: 1.6875 + x = 3.405533181 Solving 1.6875 + x = 3.405533181 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6875' to each side of the equation. 1.6875 + -1.6875 + x = 3.405533181 + -1.6875 Combine like terms: 1.6875 + -1.6875 = 0.0000 0.0000 + x = 3.405533181 + -1.6875 x = 3.405533181 + -1.6875 Combine like terms: 3.405533181 + -1.6875 = 1.718033181 x = 1.718033181 Simplifying x = 1.718033181Subproblem 2
x + 1.6875 = -3.405533181 Simplifying x + 1.6875 = -3.405533181 Reorder the terms: 1.6875 + x = -3.405533181 Solving 1.6875 + x = -3.405533181 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6875' to each side of the equation. 1.6875 + -1.6875 + x = -3.405533181 + -1.6875 Combine like terms: 1.6875 + -1.6875 = 0.0000 0.0000 + x = -3.405533181 + -1.6875 x = -3.405533181 + -1.6875 Combine like terms: -3.405533181 + -1.6875 = -5.093033181 x = -5.093033181 Simplifying x = -5.093033181Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.718033181, -5.093033181}
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