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Simplifying -5x2 + -40x + 25 = 0 Reorder the terms: 25 + -40x + -5x2 = 0 Solving 25 + -40x + -5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(5 + -8x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(5 + -8x + -1x2)' equal to zero and attempt to solve: Simplifying 5 + -8x + -1x2 = 0 Solving 5 + -8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + 8x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 8x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 8x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 8x + x2 = 0 + 5 8x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 8x + x2 = 5 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 5 + 16 Reorder the terms: 16 + 8x + x2 = 5 + 16 Combine like terms: 5 + 16 = 21 16 + 8x + x2 = 21 Factor a perfect square on the left side: (x + 4)(x + 4) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (x + 4) equal to 4.582575695 and -4.582575695.Subproblem 1
x + 4 = 4.582575695 Simplifying x + 4 = 4.582575695 Reorder the terms: 4 + x = 4.582575695 Solving 4 + x = 4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 4.582575695 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.582575695 + -4 x = 4.582575695 + -4 Combine like terms: 4.582575695 + -4 = 0.582575695 x = 0.582575695 Simplifying x = 0.582575695Subproblem 2
x + 4 = -4.582575695 Simplifying x + 4 = -4.582575695 Reorder the terms: 4 + x = -4.582575695 Solving 4 + x = -4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -4.582575695 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.582575695 + -4 x = -4.582575695 + -4 Combine like terms: -4.582575695 + -4 = -8.582575695 x = -8.582575695 Simplifying x = -8.582575695Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.582575695, -8.582575695}Solution
x = {0.582575695, -8.582575695}
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