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Simplifying (5x2) + -20x = 4 Reorder the terms: -20x + (5x2) = 4 Solving -20x + (5x2) = 4 Solving for variable 'x'. Reorder the terms: -4 + -20x + (5x2) = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -20x + (5x2) = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + -4x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -4x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -4x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -4x + x2 = 0 + 0.8 -4x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -4x + x2 = 0.8 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 0.8 + 4 Reorder the terms: 4 + -4x + x2 = 0.8 + 4 Combine like terms: 0.8 + 4 = 4.8 4 + -4x + x2 = 4.8 Factor a perfect square on the left side: ((x) + -2)((x) + -2) = 4.8 Calculate the square root of the right side: 2.19089023 Break this problem into two subproblems by setting ((x) + -2) equal to 2.19089023 and -2.19089023.Subproblem 1
(x) + -2 = 2.19089023 Simplifying (x) + -2 = 2.19089023 x + -2 = 2.19089023 Reorder the terms: -2 + x = 2.19089023 Solving -2 + x = 2.19089023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.19089023 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.19089023 + 2 x = 2.19089023 + 2 Combine like terms: 2.19089023 + 2 = 4.19089023 x = 4.19089023 Simplifying x = 4.19089023Subproblem 2
(x) + -2 = -2.19089023 Simplifying (x) + -2 = -2.19089023 x + -2 = -2.19089023 Reorder the terms: -2 + x = -2.19089023 Solving -2 + x = -2.19089023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.19089023 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.19089023 + 2 x = -2.19089023 + 2 Combine like terms: -2.19089023 + 2 = -0.19089023 x = -0.19089023 Simplifying x = -0.19089023Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.19089023, -0.19089023}
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