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Simplifying 8 = 2x2 + 10x Reorder the terms: 8 = 10x + 2x2 Solving 8 = 10x + 2x2 Solving for variable 'x'. Reorder the terms: 8 + -10x + -2x2 = 10x + -10x + 2x2 + -2x2 Combine like terms: 10x + -10x = 0 8 + -10x + -2x2 = 0 + 2x2 + -2x2 8 + -10x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 8 + -10x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -5x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -5x + -1x2)' equal to zero and attempt to solve: Simplifying 4 + -5x + -1x2 = 0 Solving 4 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + 5x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 5x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 5x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 5x + x2 = 0 + 4 5x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 5x + x2 = 4 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 4 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 4 + 6.25 Combine like terms: 4 + 6.25 = 10.25 6.25 + 5x + x2 = 10.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (x + 2.5) equal to 3.201562119 and -3.201562119.Subproblem 1
x + 2.5 = 3.201562119 Simplifying x + 2.5 = 3.201562119 Reorder the terms: 2.5 + x = 3.201562119 Solving 2.5 + x = 3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 3.201562119 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.201562119 + -2.5 x = 3.201562119 + -2.5 Combine like terms: 3.201562119 + -2.5 = 0.701562119 x = 0.701562119 Simplifying x = 0.701562119Subproblem 2
x + 2.5 = -3.201562119 Simplifying x + 2.5 = -3.201562119 Reorder the terms: 2.5 + x = -3.201562119 Solving 2.5 + x = -3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -3.201562119 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.201562119 + -2.5 x = -3.201562119 + -2.5 Combine like terms: -3.201562119 + -2.5 = -5.701562119 x = -5.701562119 Simplifying x = -5.701562119Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.701562119, -5.701562119}Solution
x = {0.701562119, -5.701562119}
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