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Simplifying 5(x + 4) * x = 4 Reorder the terms: 5(4 + x) * x = 4 Reorder the terms for easier multiplication: 5x(4 + x) = 4 (4 * 5x + x * 5x) = 4 (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 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 = 0.19089023Subproblem 2
x + 2 = -2.19089023 Simplifying 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 = -4.19089023Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.19089023, -4.19089023}
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