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Simplifying 8x2 + 2x = 110 Reorder the terms: 2x + 8x2 = 110 Solving 2x + 8x2 = 110 Solving for variable 'x'. Reorder the terms: -110 + 2x + 8x2 = 110 + -110 Combine like terms: 110 + -110 = 0 -110 + 2x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-55 + x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-55 + x + 4x2)' equal to zero and attempt to solve: Simplifying -55 + x + 4x2 = 0 Solving -55 + x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -13.75 + 0.25x + x2 = 0 Move the constant term to the right: Add '13.75' to each side of the equation. -13.75 + 0.25x + 13.75 + x2 = 0 + 13.75 Reorder the terms: -13.75 + 13.75 + 0.25x + x2 = 0 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + 0.25x + x2 = 0 + 13.75 0.25x + x2 = 0 + 13.75 Combine like terms: 0 + 13.75 = 13.75 0.25x + x2 = 13.75 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.25x + 0.25 + x2 = 13.75 + 0.25 Reorder the terms: 0.25 + 0.25x + x2 = 13.75 + 0.25 Combine like terms: 13.75 + 0.25 = 14 0.25 + 0.25x + x2 = 14 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x + 0.5) equal to 3.741657387 and -3.741657387.Subproblem 1
x + 0.5 = 3.741657387 Simplifying x + 0.5 = 3.741657387 Reorder the terms: 0.5 + x = 3.741657387 Solving 0.5 + x = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 3.741657387 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.741657387 + -0.5 x = 3.741657387 + -0.5 Combine like terms: 3.741657387 + -0.5 = 3.241657387 x = 3.241657387 Simplifying x = 3.241657387Subproblem 2
x + 0.5 = -3.741657387 Simplifying x + 0.5 = -3.741657387 Reorder the terms: 0.5 + x = -3.741657387 Solving 0.5 + x = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -3.741657387 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.741657387 + -0.5 x = -3.741657387 + -0.5 Combine like terms: -3.741657387 + -0.5 = -4.241657387 x = -4.241657387 Simplifying x = -4.241657387Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.241657387, -4.241657387}Solution
x = {3.241657387, -4.241657387}
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