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Simplifying 4x2 + 8x + -2 = 80 Reorder the terms: -2 + 8x + 4x2 = 80 Solving -2 + 8x + 4x2 = 80 Solving for variable 'x'. Reorder the terms: -2 + -80 + 8x + 4x2 = 80 + -80 Combine like terms: -2 + -80 = -82 -82 + 8x + 4x2 = 80 + -80 Combine like terms: 80 + -80 = 0 -82 + 8x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-41 + 4x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-41 + 4x + 2x2)' equal to zero and attempt to solve: Simplifying -41 + 4x + 2x2 = 0 Solving -41 + 4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -20.5 + 2x + x2 = 0 Move the constant term to the right: Add '20.5' to each side of the equation. -20.5 + 2x + 20.5 + x2 = 0 + 20.5 Reorder the terms: -20.5 + 20.5 + 2x + x2 = 0 + 20.5 Combine like terms: -20.5 + 20.5 = 0.0 0.0 + 2x + x2 = 0 + 20.5 2x + x2 = 0 + 20.5 Combine like terms: 0 + 20.5 = 20.5 2x + x2 = 20.5 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 20.5 + 1 Reorder the terms: 1 + 2x + x2 = 20.5 + 1 Combine like terms: 20.5 + 1 = 21.5 1 + 2x + x2 = 21.5 Factor a perfect square on the left side: (x + 1)(x + 1) = 21.5 Calculate the square root of the right side: 4.636809248 Break this problem into two subproblems by setting (x + 1) equal to 4.636809248 and -4.636809248.Subproblem 1
x + 1 = 4.636809248 Simplifying x + 1 = 4.636809248 Reorder the terms: 1 + x = 4.636809248 Solving 1 + x = 4.636809248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 4.636809248 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.636809248 + -1 x = 4.636809248 + -1 Combine like terms: 4.636809248 + -1 = 3.636809248 x = 3.636809248 Simplifying x = 3.636809248Subproblem 2
x + 1 = -4.636809248 Simplifying x + 1 = -4.636809248 Reorder the terms: 1 + x = -4.636809248 Solving 1 + x = -4.636809248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -4.636809248 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.636809248 + -1 x = -4.636809248 + -1 Combine like terms: -4.636809248 + -1 = -5.636809248 x = -5.636809248 Simplifying x = -5.636809248Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.636809248, -5.636809248}Solution
x = {3.636809248, -5.636809248}
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