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Simplifying 4x2 + 40x + -10 = 0 Reorder the terms: -10 + 40x + 4x2 = 0 Solving -10 + 40x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 20x + 2x2) = 0 Ignore the factor 2.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 = 27.5 25 + 10x + x2 = 27.5 Factor a perfect square on the left side: (x + 5)(x + 5) = 27.5 Calculate the square root of the right side: 5.244044241 Break this problem into two subproblems by setting (x + 5) equal to 5.244044241 and -5.244044241.Subproblem 1
x + 5 = 5.244044241 Simplifying x + 5 = 5.244044241 Reorder the terms: 5 + x = 5.244044241 Solving 5 + x = 5.244044241 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 = 5.244044241 + -5 Combine like terms: 5 + -5 = 0 0 + x = 5.244044241 + -5 x = 5.244044241 + -5 Combine like terms: 5.244044241 + -5 = 0.244044241 x = 0.244044241 Simplifying x = 0.244044241Subproblem 2
x + 5 = -5.244044241 Simplifying x + 5 = -5.244044241 Reorder the terms: 5 + x = -5.244044241 Solving 5 + x = -5.244044241 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 = -5.244044241 + -5 Combine like terms: 5 + -5 = 0 0 + x = -5.244044241 + -5 x = -5.244044241 + -5 Combine like terms: -5.244044241 + -5 = -10.244044241 x = -10.244044241 Simplifying x = -10.244044241Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.244044241, -10.244044241}Solution
x = {0.244044241, -10.244044241}
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