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Simplifying 5 = 20x + (10x * x) Multiply x * x 5 = 20x + (10x2) Solving 5 = 20x + (10x2) Solving for variable 'x'. Reorder the terms: 5 + -20x + (-10x2) = 20x + -20x + (10x2) + (-10x2) Combine like terms: 20x + -20x = 0 5 + -20x + (-10x2) = 0 + (10x2) + (-10x2) 5 + -20x + (-10x2) = (10x2) + (-10x2) Combine like terms: (10x2) + (-10x2) = 0 5 + -20x + (-10x2) = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(1 + -4x + (-2x2)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + -4x + (-2x2))' equal to zero and attempt to solve: Simplifying 1 + -4x + (-2x2) = 0 Solving 1 + -4x + (-2x2) = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.5 + 2x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 2x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 2x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 2x + x2 = 0 + 0.5 2x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 2x + x2 = 0.5 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 = 0.5 + 1 Reorder the terms: 1 + 2x + x2 = 0.5 + 1 Combine like terms: 0.5 + 1 = 1.5 1 + 2x + x2 = 1.5 Factor a perfect square on the left side: ((x) + 1)((x) + 1) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting ((x) + 1) equal to 1.224744871 and -1.224744871.Subproblem 1
(x) + 1 = 1.224744871 Simplifying (x) + 1 = 1.224744871 x + 1 = 1.224744871 Reorder the terms: 1 + x = 1.224744871 Solving 1 + x = 1.224744871 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 = 1.224744871 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.224744871 + -1 x = 1.224744871 + -1 Combine like terms: 1.224744871 + -1 = 0.224744871 x = 0.224744871 Simplifying x = 0.224744871Subproblem 2
(x) + 1 = -1.224744871 Simplifying (x) + 1 = -1.224744871 x + 1 = -1.224744871 Reorder the terms: 1 + x = -1.224744871 Solving 1 + x = -1.224744871 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 = -1.224744871 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.224744871 + -1 x = -1.224744871 + -1 Combine like terms: -1.224744871 + -1 = -2.224744871 x = -2.224744871 Simplifying x = -2.224744871Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.224744871, -2.224744871}Solution
x = {0.224744871, -2.224744871}
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