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Simplifying 0.4x(8 + -0.2x) = -4 (8 * 0.4x + -0.2x * 0.4x) = -4 (3.2x + -0.08x2) = -4 Solving 3.2x + -0.08x2 = -4 Solving for variable 'x'. Reorder the terms: 4 + 3.2x + -0.08x2 = -4 + 4 Combine like terms: -4 + 4 = 0 4 + 3.2x + -0.08x2 = 0 Begin completing the square. Divide all terms by -0.08 the coefficient of the squared term: Divide each side by '-0.08'. -50 + -40x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + -40x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + -40x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -40x + x2 = 0 + 50 -40x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 -40x + x2 = 50 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = 50 + 400 Reorder the terms: 400 + -40x + x2 = 50 + 400 Combine like terms: 50 + 400 = 450 400 + -40x + x2 = 450 Factor a perfect square on the left side: (x + -20)(x + -20) = 450 Calculate the square root of the right side: 21.213203436 Break this problem into two subproblems by setting (x + -20) equal to 21.213203436 and -21.213203436.Subproblem 1
x + -20 = 21.213203436 Simplifying x + -20 = 21.213203436 Reorder the terms: -20 + x = 21.213203436 Solving -20 + x = 21.213203436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 21.213203436 + 20 Combine like terms: -20 + 20 = 0 0 + x = 21.213203436 + 20 x = 21.213203436 + 20 Combine like terms: 21.213203436 + 20 = 41.213203436 x = 41.213203436 Simplifying x = 41.213203436Subproblem 2
x + -20 = -21.213203436 Simplifying x + -20 = -21.213203436 Reorder the terms: -20 + x = -21.213203436 Solving -20 + x = -21.213203436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -21.213203436 + 20 Combine like terms: -20 + 20 = 0 0 + x = -21.213203436 + 20 x = -21.213203436 + 20 Combine like terms: -21.213203436 + 20 = -1.213203436 x = -1.213203436 Simplifying x = -1.213203436Solution
The solution to the problem is based on the solutions from the subproblems. x = {41.213203436, -1.213203436}
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