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Simplifying -2x2 + -20x = 5 Reorder the terms: -20x + -2x2 = 5 Solving -20x + -2x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + -20x + -2x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -20x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 20x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 20x + 2x2)' equal to zero and attempt to solve: Simplifying 5 + 20x + 2x2 = 0 Solving 5 + 20x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + 10x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 10x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 10x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 10x + x2 = 0 + -2.5 10x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 10x + x2 = -2.5 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -2.5 + 25 Reorder the terms: 25 + 10x + x2 = -2.5 + 25 Combine like terms: -2.5 + 25 = 22.5 25 + 10x + x2 = 22.5 Factor a perfect square on the left side: (x + 5)(x + 5) = 22.5 Calculate the square root of the right side: 4.74341649 Break this problem into two subproblems by setting (x + 5) equal to 4.74341649 and -4.74341649.Subproblem 1
x + 5 = 4.74341649 Simplifying x + 5 = 4.74341649 Reorder the terms: 5 + x = 4.74341649 Solving 5 + x = 4.74341649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 4.74341649 + -5 Combine like terms: 5 + -5 = 0 0 + x = 4.74341649 + -5 x = 4.74341649 + -5 Combine like terms: 4.74341649 + -5 = -0.25658351 x = -0.25658351 Simplifying x = -0.25658351Subproblem 2
x + 5 = -4.74341649 Simplifying x + 5 = -4.74341649 Reorder the terms: 5 + x = -4.74341649 Solving 5 + x = -4.74341649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -4.74341649 + -5 Combine like terms: 5 + -5 = 0 0 + x = -4.74341649 + -5 x = -4.74341649 + -5 Combine like terms: -4.74341649 + -5 = -9.74341649 x = -9.74341649 Simplifying x = -9.74341649Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.25658351, -9.74341649}Solution
x = {-0.25658351, -9.74341649}
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